Jia Liu, Jiaxin Luo, Weiwen Xu, Jonathan M. Garibaldi, Xiao-Kun Wu, Yixue Hao, Min Chen. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

The universality of deep neural networks across different modalities and their generalization capabilities to unseen domains play an essential role in medical image segmentation. The recent segment anything model (SAM) has demonstrated strong adaptability across diverse natural scenarios. However, the huge computational costs, demand for manual annotations as prompts and conflict-prone decoding process of SAM degrade its generalization capabilities in medical scenarios. To address these limitations, we propose a modality-decoupled lightweight SAM for domain-generalized medical image segmentation, named De-LightSAM. Specifically, we first devise a lightweight domain-controllable image encoder (DC-Encoder) that produces discriminative visual features for diverse modalities. Further, we introduce the self-patch prompt generator (SP-Generator) to automatically generate high-quality dense prompt embeddings for guiding segmentation decoding. Finally, we design the query-decoupled modality decoder (QM-Decoder) that leverages a one-to-one strategy to provide an independent decoding channel for every modality, preventing mutual knowledge interference of different modalities. Moreover, we design a multi-modal decoupled knowledge distillation (MDKD) strategy to leverage robust common knowledge to complement domain-specific medical feature representations. Extensive experiments indicate that De-LightSAM outperforms state-of-the-arts in diverse medical imaging segmentation tasks, displaying superior modality universality and generalization capabilities. Especially, De-LightSAM uses only 2.0% parameters compared to SAM-H. The source code is available at https://github.com/xq141839/De-LightSAM.

The design of membership functions in fuzzy systems often requires satisfying domain, semantic, and relational constraints. Existing methods, while effective at enforcing parameter bounds, often lack flexibility or fail to address complex relational constraints. To overcome these limitations, this paper introduces the Constraints Always Satisfied Parameters (CASPs) framework, which inherently satisfies constraints during optimisation. Three variants of the CASPs are proposed, each balancing design flexibility, performance, and interpretability differently. Experimental evaluations on the Electricity and Laser datasets demonstrate consistent constraint satisfaction across all runs, with CASPs-Single prioritising interpretability, CASPs-Free excelling in RMSE performance, and CASPs-Adapted offering a balanced approach. The results highlight the potential of CASPs to enhance the design and optimisation of fuzzy systems.

Concept drift detection (CDD) is the general problem of identifying significant changes in streaming data distribution over time. Effective drift detection is important in industrial processes such as oil and gas exploration to mitigate financial losses, ensure personnel safety, and reduce environmental risks. However, current CDD methods face challenges in large-scale, multivariate datasets, where single drift detectors (DD) often fail to capture variable interdependencies. While ensemble drift detectors (EDD) are usually adopted to mitigate the adoption of a single DD, EDD may suffer when detections do not converge. This misalignment can cause voting mechanisms to neglect critical intervals with high detection rates. To address this issue, we propose a fuzzy ensemble drift detector (FEDD) that integrates unsupervised threshold voting with fuzzy logic to provide time tolerance and reconcile minor temporal misalignments in drift detection. FEDD is evaluated using the 3W dataset, a realistic public benchmark with rare undesirable real events in oil wells. The results demonstrate that FEDD outperforms existing approaches by improving detection robustness and coverage, ensuring more reliable drift detection in high-dimensional, noisy environments.

The online bin packing problem is a well-known optimization challenge that finds application in a wide range of real-world scenarios. In the paper, we propose a novel algorithm called FuzzyPatternPack(FPP), which leverages fuzzy inference and pattern-based predictions of the distribution of item sizes in online bin packing. In comparison to traditional heuristics like BestFit(BF) and FirstFit(FF), as well as the more recent PatternPack(PaP) and ProfilePacking(PrP) algorithm based on online predictions, FPP demonstrates competitive and superior performance in solving various benchmark problems. Particularly, it excels in addressing problems with evolving distributions, making it a promising solution for real-world applications where the item sizes may change over time. This research unveils the promising potential of employing fuzzy logic to effectively address uncertainty in scheduling and planning problems.

The loss function plays an important role in deep learning models as it determines the model convergence behavior and performance. In semantic segmentation, many methods utilize pixel-wise (e.g. cross-entropy) and region-wise (e.g. dice) losses while boundary-wise loss is underexplored. It is known that one of the key aims of semantic segmentation is to precisely delineate objects' boundaries. Hence, it is essential to design a loss function that measures the errors around objects' boundaries. Fuzzy rough sets are constituted by the fuzzy equivalence relation, which is commonly used to measure the difference between two sets. In this paper, the lower approximation of fuzzy rough sets is proposed to construct the boundary-wise loss in deep learning models for the first time. The experiments with various segmentation models and datasets have verified that the proposed fuzzy rough sets loss is superior to other boundary-wise losses in terms of segmentation accuracy and time complexity. Compared with the commonly used pixel-wise and region-wise losses, the proposed boundary-wise loss performs similarly in dice coefficient, pixel-wise accuracy, but has a better performance in Hausdorff distance and symmetric surface distance. It indicates that the proposed loss provides a better guidance for segmentation models in producing more accurate shapes of the target objects.

The rules of a rule-based system provide explanations for its behavior by revealing the relationships between the variables captured. However, ideally, we have AI systems which go beyond explainable AI (XAI), that is, systems which not only explain their behavior, but also communicate their “insights” with respect to the real world. This requires rules to capture causal relationships between variables. In this article, we argue that those systems where the rules reflect causal relationships between variables represent an important class of fuzzy rule-based systems with unique benefits. Specifically, such systems benefit from improved performance and robustness; facilitate global explainability and thus cater to a core ambition for AI: the ability to communicate important relationships among a system's real-world variables to the human users of AI. We establish two causal-rule focused approaches to design fuzzy systems, and show the distinctions in their respective application scenarios for the explanations of the rules obtained by these two methods. The results show that rules which reflect causal relationships are more suitable for XAI than rules which “only” reflect correlations, while also confirming that they offer robustness to over-fitting, in turn supporting strong performance.

Currently, type-2 fuzzy systems, fuzzy control strategies, and origami structures have been used in robots to assist in the comfortable and smooth operation of such robots. Recent advances in these various fields have been employed to improve the key technologies of wearable robots, such as providing more efficient decision making, improved maneuverability, increased control intelligence, and more lightweight structures. The current advances have highlighted the potential for these various methods, both separately and in combination with each other, to achieve further significant advances. Hence, this article summarizes the latest research results in these three key aspects, elaborates on some of the challenges that remain, and discusses potential development directions of wearable robots in the future.

Deep learning methods have achieved an excellent performance in medical image segmentation. However, the practical application of deep learning-based segmentation models is limited in clinical settings due to the lack of reliable information about the segmentation quality. In this article, we propose a novel quality control algorithm based on fuzzy uncertainty to quantify the quality of the predicted segmentation results as part of the model inference process. First, test-time augmentation and Monte Carlo dropout are applied simultaneously to capture both the data and model uncertainties of the trained image segmentation model. Then, a fuzzy set is generated to describe the captured uncertainty with the assistance of the linear Euclidean distance transform algorithm. Finally, the fuzziness of the generated fuzzy set is adopted to calculate an image-level segmentation uncertainty and, therefore, to infer the segmentation quality. Extensive experiments using five medical image segmentation applications on the detection of skin lesion, nuclei, lung, breast, and cell are conducted to evaluate the proposed algorithm. The experimental results show that the estimated image-level uncertainties using the proposed method have strong correlations with the segmentation qualities measured by the Dice coefficient, resulting in absolute Pearson correlation coefficients of 0.60–0.92. Our method outperforms other five state-of-the-art quality control methods in classifying the segmentation results into good and poor quality groups (area under the receiver operating curve of greater than 0.92, while other methods are below 0.85).

Deep convolutional neural networks (DCNN)-based methods have achieved promising performance in semantic image segmentation. However, in practical applications, it is important not only to produce the segmentation result but also to inform the segmentation quality (e.g. confidence of the segmentation result). In this paper, we propose to utilize fuzzy sets for estimating segmentation uncertainty, therefore to infer the quality of segmentation produced by a DCNN model. The proposed method combines test-time augmentation and fuzzy sets to estimate an image-level uncertainty. Six different fuzziness measures are implemented and compared, in order to select the best fuzzy uncertainty metric for the proposed method. A public skin lesion dataset is used to evaluate the method. The results show a strong correlation (Pearson correlation coefficient of 0.736) between our proposed uncertainty measure and image segmentation quality measured by Dice coefficient.

Mango is the third most crucial fruit product worldwide in terms of value and production volume, after pineapple and banana. However, assessing the quality grading of mangoes in an agricultural environment as a manual task is inefficient, labour demanding, and prone to errors. Thus, this task entails uncertainty in human decision-making, i.e. choice subjectivity due to a diverse perspective, experience, and knowledge. When dealing with ambiguity, fuzzy logic systems (FLSs) can help aid in the systematic automation of the human grading system. However, the underlying problem with FLSs is that they have difficulty dealing with large and complex real-world situations, in which in the curse of dimensionality is an issue. A possible option is to employ a hierarchical fuzzy system, a subtype of an FLS that is particularly effective in reducing the complexity and increasing the interpretability of the overall system. This study proposes an approach to model uncertainty in mango grading decision-making using a hierarchical fuzzy system. We demonstrate the HFS for mango grading application using a FuzzyR toolkit, together with an FLS for comparison. Additionally, this paper explores the importance of uncertainty arising from human knowledge, which will be critical in determining the most suitable system (FLS or HFS) closest to the experts’ opinion. Additionally, we also evaluate both systems’ interpretability.

EXplainable Artificial Intelligence (XAI) is of in-creasing importance as researchers and practitioners seek better transparency and verifiability of AI systems. Mamdani fuzzy systems can provide explanations based on their linguistic rules, and thus a potential pathway to XAI. A factual rule based explanation generally refers to the given set of rules executed, or fired, for a given input. However, research has shown that human explanations are often counterfactual (CF), i.e. rather than explaining why a given output was reached, they show why other potential outputs were not. Although several machine learning-based CF explanation generation methods have been proposed in recent years, quasi none of them focus on fuzzy systems. Also, where they do, they focus on correlation, which limits the interpretive value of any CF explanations obtained as humans expect a causal relationship in rules, i.e. we are cause-effect thinkers. In this paper, we propose a new rule generation framework for Mamdani fuzzy classification systems, which we refer to as CF-MABLAR, building on the MARkov BLAnket Rules (MABLAR) framework. CF-MABLAR approximates the causal links between inputs and output(s) of fuzzy systems and generates CF rules by leveraging them. Uniquely, the CF rules obtained not only provide a basic CF explanation, but can also articulate how the given inputs would need to be changed to generate a different output, crucial for lay-user insight, verification and sensitivity-evaluation of XAI systems, for example in decision support around credit risk, cyber security and medical assistance.

In medical image segmentation, supervised machine learning models trained using one image modality (e.g. computed tomography (CT)) are often prone to failure when applied to another image modality (e.g. magnetic resonance imaging (MRI)) even for the same organ. This is due to the significant intensity variations of different image modalities. In this paper, we propose a novel end-to-end deep neural network to achieve multi-modality image segmentation, where image labels of only one modality (source domain) are available for model training and the image labels for the other modality (target domain) are not available. In our method, a multi-resolution locally normalized gradient magnitude approach is firstly applied to images of both domains for minimizing the intensity discrepancy. Subsequently, a dual task encoder-decoder network including image segmentation and reconstruction is utilized to effectively adapt a segmentation network to the unlabeled target domain. Additionally, a shape constraint is imposed by leveraging adversarial learning. Finally, images from the target domain are segmented, as the network learns a consistent latent feature representation with shape awareness from both domains. We implement both 2D and 3D versions of our method, in which we evaluate CT and MRI images for kidney and cardiac tissue segmentation. For kidney, a public CT dataset (KiTS19, MICCAI 2019) and a local MRI dataset were utilized. The cardiac dataset was from the Multi-Modality Whole Heart Segmentation (MMWHS) challenge 2017. Experimental results reveal that our proposed method achieves significantly higher performance with a much lower model complexity in comparison with other state-of-the-art methods. More importantly, our method is also capable of producing superior segmentation results than other methods for images of an unseen target domain without model retraining. The code is available at GitHub (https://github.com/MinaJf/LMISA) to encourage method comparison and further research.

Data obtained from the real-world tends to be uncertain: Measurement inaccuracies, variability in opinions, and human errors are just some of the reasons that make the information collection process noisy. In recent years, fuzzy sets have been used to capture the uncertainty in data and then build automatic reasoning systems. In some contexts, data on a given subject is gathered from multiple sources and each instance modeled through a fuzzy set. A typical example of this scenario is represented by surveys, in which many participants express their opinions on the same topics. The fuzzy sets representing individual instances can be combined in a new (type-1 or type-2) fuzzy set in order to capture expert or measurement variation. In this article, we propose a novel approach which combines uncertain data modeled through parametric fuzzy sets in an intuitive manner, using the recently introducedconstrained interval type-2 (IT2) fuzzy sets. By intuitive, we mean that each resultant constrained IT2 fuzzy set preserves the shape used to represent a single data instance, while making use of the footprint of uncertainty to represent uncertainty around its parameters. This novelconstrained parametric approachis applied to interval-valued data gathered from real surveys and compared to the other algorithms in the literature, showing how it differs from them, with discussion of the contexts in which it represents a valuable alternative. Finally, it is shown how this novel approach can be used to model not just intervals but data in which individual instances can be modeled through any parametric fuzzy sets (e.g., triangular).

In this work, we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence functions allow us to compare any two general type-2 fuzzy sets and to generate a similarity measure for type-2 fuzzy sets. The result of this similarity is a fuzzy set on the same referential set (i.e., domain) as the considered type-2 fuzzy set. The latter is crucial for applications such as explainable AI and decision-making, as it enables an intuitive interpretation of the similarity within the domain-specific context of the fuzzy sets. We show how this measure can be used to compare type-2 fuzzy sets with different membership functions in such a way that the uncertainty linked to type-2 fuzzy sets is not lost. This is achieved by generating a fuzzy set rather than a single numerical value. Furthermore, we also show how to obtain a numerical value for discrete referential sets.

Network security requires effective detection and proper analysis of abnormal network behavior. To address the uncertainty associated with the process of network intrusion detection, this article proposes a network intrusion-detection algorithm based on dynamic intuitionistic fuzzy sets (IFSs). We use the classic network intrusion datasets KDD 99, NSL-KDD, and the massive, high-dimensional dataset UNSW-NB15 to evaluate the performance of our proposed algorithm. First, we perform data preprocessing on these three datasets and select features based on the results of a chi-square test. Second, using time-series processing, we construct dynamic intuitionistic fuzzy patterns from the feature-selected datasets. At last, we use a proposed distance measure for the dynamic IFSs to generate a classifier that facilitates the detection of network intrusion. Experimental results show that the classification performance of the proposed algorithm is superior to that of other state-of-the-art algorithms on the three aforementioned datasets. The achieved improvement in classification performance is particularly significant for large datasets.

Recent years have seen a surge in interest in non-singleton fuzzy systems. These systems enable the direct modelling of uncertainty affecting systems' inputs using the fuzzification stage. Moreover, recent work has shown how different composition approaches to modelling the interaction between the non-singleton input and the antecedent fuzzy sets enable the efficient handling of uncertainty without requiring changes in a system's rule base, with benefits both in terms of performance and interpretability. As thus far few current software toolkit support non-singleton fuzzy systems, this paper presents an extension of the FuzzyR toolbox, which is a freely available R package on CRAN, for non-singleton fuzzy logic systems. The updated toolbox enables a non-singleton model to be conveniently built from scratch, or for existing singleton fuzzy logic systems built using FuzzyR to be converted easily. Predefined operations include fuzzification of crisp inputs (e.g. into Gaussian membership functions), and a variety of composition approaches for computing rules' firing-strengths, based on the standard, centroid-based, and similarity-based methods. It is also possible to include user-defined options for these abovementioned methods, without the need to modify (or update) the FuzzyR toolbox itself. In this paper, detailed introductions for the new non-singleton features of the toolkit are presented, complete with code samples in R to facilitate adoption both within and beyond the community. Further, the paper presents a series of validation experiments, replicating a recent empirical analysis of non-singleton fuzzy logic systems in the context of time-series prediction with different levels of noise.

Convolutional neural networks (CNNs) have achieved the state-of-the-art performance in many application areas, due to the capability of automatically extracting and aggregating spatial and channel-wise features from images. Most recent studies have concentrated on modifying convolutional kernel size to achieve multi-scale spatial information. In this paper, we introduce a novel fuzzy integral module to the CNNs for fusing the information across feature channels. The fuzzy integral is a mathematical aggregation operator and is widely used in decision level fusion. Herein, we utilize a special case of fuzzy integrals namely ordered weight averaging (OWA) to merge information at feature level. Three publicly available datasets were used to evaluate the proposed fuzzy CNN model for image segmentation. The results show that the proposed fuzzy module helps in reducing the baseline model parameters by 58.54% while producing higher segmentation accuracy (measured by Dice) than the baseline method and a similar method reported in the literature.

The use of Hierarchical Fuzzy Systems (HFS) has been well acknowledged as a good approach in reducing the complexity and improving the interpretability of fuzzy logic systems (FLS). Over the past years, many fuzzy logic toolkits have been made available for type-1, interval type-2 and general type-2 fuzzy logic systems under different programming languages. However, it is still challenging for people, especially for those who are not expert in fuzzy systems or programming, to build models based on HFSs. The main reason could be the lack of practical tools and examples of using HFSs. This paper presents a step-by-step guide to the implementation of an HFS with the open-source toolbox, FuzzyR, utilising the R Programming Language.

A novel ensemble feature selection (FS) framework using fuzzy aggregation is proposed in this paper. It consists of three main steps: distribution generation of feature importance, distribution ensemble using fuzzy aggregation, and defuzzification for feature ranking. Based on four state-of-the-art FS methods (named as base selectors in our algorithm) selected from different method categories, different fuzzy aggregation operators were implemented to achieve ensemble learning for decision making. A training data repository that consists of eight datasets was used for parameter tuning of the proposed framework. The proposed framework using drastic sum aggregation achieved the best performance and was subsequently evaluated on eight independent testing datasets. Remarkably, the proposed method achieved the best classification accuracy and the highest stability compared with the four base FS methods. It also outperformed our previously proposed score based ensemble method [1].

Improving the efficiency of type-reduction algorithms continues to attract research interest. Recently, there has been some new type-reduction approaches claiming that they are more efficient than the well-known algorithms such as the enhanced Karnik–Mendel (EKM) and the enhanced iterative algorithm with stopping condition (EIASC). In a previous paper, we found that the computational efficiency of an algorithm is closely related to the platform, and how it is implemented. In computer science, the dependence on languages is usually avoided by focusing on the complexity of algorithms (using big O notation). In this article, the main contribution is the proposal of two novel type-reduction algorithms. Also, for the first time, a comprehensive study on both existing and new type-reduction approaches is made based on both algorithm complexity and practical computational time under a variety of programming languages. Based on the results, suggestions are given for the preferred algorithms in different scenarios depending on implementation platform and application context.

In many contexts, type-2 fuzzy sets (T2 FS) are obtained from a type-1 fuzzy set to which we wish to add uncertainty. However, in the current type-2 representation, there is no restriction on the shape of the footprint of uncertainty and the embedded sets (ESs) that can be considered acceptable. This leads, usually, to the loss of the semantic relationship between the T2 FS and the concept it models. As a consequence, the interpretability of some of the ESs and the explainability of the uncertainty measures obtained from them can decrease. To overcome these issues, constrained type-2 (CT2) fuzzy sets have been proposed. However, no formal definitions for some of their key components [e.g., acceptable ESs (AESs)] and constrained operations have been given. In this article, we provide some theoretical underpinning for the definition of CT2 sets, their inferencing and defuzzification method. To conclude, the constrained inference framework is presented, applied to two real-world cases and briefly compared to the standard interval type-2 inference and defuzzification method.

Constrained interval type-2 (CIT2) fuzzy sets have been introduced to preserve interpretability when moving from type-1 to interval type-2 (IT2) membership functions. Although they can be used to produce type-2 fuzzy systems with enhanced explainability, so far, the latter comes at the expense of high computational cost. Specifically, the exhaustive type-reduction method for CIT2 Mamdani systems has been shown to be too slow to be used in practical applications and even the current approximation procedure is much slower than modern type-reduction algorithms used for IT2 fuzzy sets. In this article, a novel type-reduction procedure for CIT2 sets is presented, based on the concept of switch indices. The algorithm is applied on a real-world classification problem and compared to other type-reduction approaches used in IT2 and CIT2 systems. In the case studies presented, the new algorithm is significantly faster than the exhaustive and sampling CIT2 approaches while keeping the high level of interpretability of the type-reduction operation that characterizes CIT2 fuzzy sets.

Hierarchical fuzzy systems (HFSs) have been shown to have the potential to improve the interpretability of fuzzy logic systems (FLSs). However, challenges remain, such as “How can we measure their interpretability?” “How can we make an informed assessment of how HFSs should be designed to enhance interpretability?” The challenges consist of measuring the interpretability of HFSs include issues such as their topological structure, the number of layers, the meaning of intermediate variables, and so on. In this article, an initial framework to measure the interpretability of HFSs is proposed, combined with a participatory user design process to create a specific instance of the framework for an application context. This approach enables the subjective views of a range of practitioners, experts in the design and creation of FLSs, to be taken into account in shaping the design of a generic framework for measuring interpretability in HFSs. This design process and framework are demonstrated through two classification application examples, showing the ability of the resulting index to appropriately capture interpretability as perceived by system design experts.

The type-1 ordered weighted averaging (T1OWA) operator has demonstrated the capacity for directly aggregating multiple sources of linguistic information modeled by fuzzy sets rather than crisp values. Yager's ordered weighted averaging (OWA) operators possess the properties of idempotence, monotonicity, compensativeness, and commutativity. This article aims to address whether or not T1OWA operators possess these properties when the inputs and associated weights are fuzzy sets instead of crisp numbers. To this end, a partially ordered relation of fuzzy sets is defined based on the fuzzy maximum (join) and fuzzy minimum (meet) operators of fuzzy sets, and an alpha-equivalently-ordered relation of groups of fuzzy sets is proposed. Moreover, as the extension of orness and andness of an Yager's OWA operator, joinness and meetness of a T1OWA operator are formalized, respectively. Then, based on these concepts and the representation theorem of T1OWA operators, we prove that T1OWA operators hold the same properties as Yager's OWA operators possess, i.e., idempotence, monotonicity, compensativeness, and commutativity. Various numerical examples and a case study of diabetes diagnosis are provided to validate the theoretical analyses of these properties in aggregating multiple sources of uncertain information and improving integrated diagnosis, respectively.

Accurately locating the fovea is a prerequisite for developing computer aided diagnosis (CAD) of retinal diseases. In colour fundus images of the retina, the fovea is a fuzzy region lacking prominent visual features and this makes it difficult to directly locate the fovea. While traditional methods rely on explicitly extracting image features from the surrounding structures such as the optic disc and various vessels to infer the position of the fovea, deep learning based regression technique can implicitly model the relation between the fovea and other nearby anatomical structures to determine the location of the fovea in an end-to-end fashion. Although promising, using deep learning for fovea localisation also has many unsolved challenges. In this paper, we present a new end-to-end fovea localisation method based on a hierarchical coarse-to-fine deep regression neural network. The innovative features of the new method include a multi-scale feature fusion technique and a self-attention technique to exploit location, semantic, and contextual information in an integrated framework, a multi-field-of-view (multi-FOV) feature fusion technique for context-aware feature learning and a Gaussian-shift-cropping method for augmenting effective training data. We present extensive experimental results on two public databases and show that our new method achieved state-of-the-art performances. We also present a comprehensive ablation study and analysis to demonstrate the technical soundness and effectiveness of the overall framework and its various constituent components.

This paper presents an R package FuzzyR which is an extended fuzzy logic toolbox for the R programming language. FuzzyR is a continuation of the previous Fuzzy R toolboxes such as FuzzyToolkitUoN. Whilst keeping existing functionalities of the previous toolboxes, the main extension in the FuzzyR toolbox is the capability of optimising type-1 and interval type-2 fuzzy inference systems based on an extended ANFIS architecture. An accuracy function is also added to provide performance indicators featuring eight alternative accuracy measures, including a new measure UMBRAE. In addition, graphical user interfaces have been provided so that the properties of a fuzzy inference system can be visualised and manipulated, which is particularly useful for teaching and learning. Note that this paper illustrates some of the new features of the FuzzyR toolbox, but does not provide a complete list of all functions available. More details about the new features of FuzzyR and a complete description of all functions can be found in the manual of the toolbox.

In recent year, there has been a growing need for intelligent systems that not only are able to provide reliable classifications but can also produce explanations for the decisions they make. The demand for increased explainability has led to the emergence of explainable artificial intelligence (XAI) as a specific research field. In this context, fuzzy logic systems represent a promising tool thanks to their inherently interpretable structure. The use of a rule-base and linguistic terms, in fact, have allowed researchers to create models that are able to produce explanations in natural language for each of the classifications they make. So far, however, designing systems that make use of interval type-2 (IT2) fuzzy logic and also give explanations for their outputs has been very challenging, partially due to the presence of the type-reduction step. In this paper, it will be shown how constrained interval type-2 (CIT2) fuzzy sets represent a valid alternative to conventional interval type-2 sets in order to address this issue. Through the analysis of two case studies from the medical domain, it is shown how explainable CIT2 classifiers are produced. These systems can explain which rules contributed to the creation of each of the endpoints of the output interval centroid, while showing (in these examples) the same level of accuracy as their IT2 counterpart.

Constrained interval type-2 (CIT2) fuzzy sets are a class of type-2 fuzzy sets that has been recently proposed as a way to extend type-1 membership functions to interval type-2 (IT2) while keeping a semantic connection between the IT2 fuzzy set and the concept it models. Recent work has shown how their mathematical properties can be used to design CIT2 fuzzy logic systems that are able to provide explanations for their outputs. Although the CIT2 representation can be a valuable alternative to the IT2 one, no software library for their implementation is available for the research community. The aim of this paper is to introduce a new Java library, Juzzy Constrained, that has been developed as an extension of the popular type-1 and type-2 Java toolkit Juzzy, adding support for CIT2 sets and systems. Throughout the paper, the main classes and the structure of the new library are described, together with a working example that illustrates how to build a CIT2 fuzzy system from scratch and how it can be used to produce explanations for the output.

Interpretability is an important and necessary topic that needs to be discussed in relation to the fields of Artificial Intelligence and Machine Learning. Within fuzzy logic systems (FLSs), hierarchical fuzzy systems (HFSs) have been suggested as a key component to help improve the interpretability of FLSs. In this context, complexity is a key component in the interpretability of FLSs. In FLSs, the complexity is commonly expressed using in a rule-based manner, considering the number of rules, variables, and fuzzy terms. Several studies have used indicators (for example, the number of rules) to measure the complexity of FLSs. However, this is not a perfect way of assessing complexity in HFSs that have the structure of multiple subsystems, layers and different topologies. Thus far, complexity assessment associated with the structure of HFSs has not been discussed. In this paper, we aim to put forward a new approach in assessing the complexity of HFSs, which will combine rule-based complexity and structural complexity. A detailed measurement of complexity for different HFSs' topologies, namely parallel and serial, will be presented to showcase the features of the new approach. The contribution of this paper is the introduction of a combined rule-based and structural complexities-based approach in order to establish a comprehensive measurement of complexity in HFSs.

This paper presents a novel meta learning framework for feature selection (FS) based on fuzzy similarity. The proposed method aims to recommend the best FS method from four candidate FS methods for any given dataset. This is achieved by firstly constructing a large training data repository using data synthesis. Six meta features that represent the characteristics of the training dataset are then extracted. The best FS method for each of the training datasets is used as the meta label. Both the meta features and the corresponding meta labels are subsequently used to train a classification model using a fuzzy similarity measure based framework. Finally the trained model is used to recommend the most suitable FS method for a given unseen dataset. This proposed method was evaluated based on eight public datasets of real-world applications. It successfully recommended the best method for five datasets and the second best method for one dataset, which outperformed any of the four individual FS methods. Besides, the proposed method is computationally efficient for algorithm selection, leading to negligible additional time for the feature selection process. Thus, the paper contributes a novel method for effectively recommending which feature selection method to use for any new given dataset.

Nonsingleton fuzzy logic systems (NSFLSs) have the potential to capture and handle input noise within the design of input fuzzy sets (FSs). In this article, we propose an online learning method that utilizes a sequence of observations to continuously update the input FSs of an NSFLS, thus providing an improved capacity to deal with variations in the level of input-affecting noise, common in real-world applications. The method removes the requirement for both a priori knowledge of noise levels and relying on offline training procedures to define input FS parameters. To the best of our knowledge, the proposed ADaptive, ONline Nonsingleton (ADONiS) fuzzy logic system (FLS) framework represents the first end-to-end framework to adaptively configure nonsingleton input FSs. The latter is achieved through online uncertainty detection applied to a sliding window of observations. Since real-world environments are influenced by a broad range of noise sources, which can vary greatly in magnitude over time, the proposed technique for combining online determination of noise levels with associated adaptation of input FSs provides an efficient and effective solution which elegantly models input uncertainty in the FLS's input FSs, without requiring changes in any other part (e.g., antecedents, rules or consequents) of the FLS. In this article, two common chaotic time series (Mackey-Glass, Lorenz) are used to perform prediction experiments to demonstrate and evaluate the proposed framework. Results indicate that the proposed adaptive NSFLS framework provides significant advantages, particularly in environments that include high variation in noise levels, which are common in real-world applications.

Deep learning models often use a flat softmax layer to classify samples after feature extraction in visual classification tasks. However, it is hard to make a single decision of finding the true label from massive classes. In this scenario, hierarchical classification is proved to be an effective solution and can be utilized to replace the softmax layer. A key issue of hierarchical classification is to construct a good label structure, which is very significant for classification performance. Several works have been proposed to address the issue, but they have some limitations and are almost designed heuristically. In this article, inspired by fuzzy rough set theory, we propose a deep fuzzy tree model which learns a better tree structure and classifiers for hierarchical classification with theory guarantee. Experimental results show the effectiveness and efficiency of the proposed model in various visual classification datasets.

Deep learning approaches are widely applied to histopathological image analysis due to the impressive levels of performance achieved. However, when dealing with high-resolution histopathological images, utilizing the original image as input to the deep learning model is computationally expensive, while resizing the original image to achieve low resolution incurs information loss. Some hard-attention based approaches have emerged to select possible lesion regions from images to avoid processing the original image. However, these hard-attention based approaches usually take a long time to converge with weak guidance, and valueless patches may be trained by the classifier. To overcome this problem, we propose a deep selective attention approach that aims to select valuable regions in the original images for classification. In our approach, a decision network is developed to decide where to crop and whether the cropped patch is necessary for classification. These selected patches are then trained by the classification network, which then provides feedback to the decision network to update its selection policy. With such a co-evolution training strategy, we show that our approach can achieve a fast convergence rate and high classification accuracy. Our approach is evaluated on a public breast cancer histopathological image database, where it demonstrates superior performance compared to state-of-the-art deep learning approaches, achieving approximately 98% classification accuracy while only taking 50% of the training time of the previous hard-attention approach.

Current methods to identify cut-off values for tumour-associated molecules (antigens) discrimination are based on statistics and brute force. These methods applied to cancer screening problems are very inefficient, especially with large data sets with many antigens being investigated. There is a long wait to produce outcomes for clinicians, high performance computing is required, the best solution is not likely to be achieved and scalability is an issue. Cancer research is therefore limited in the number of antigens the methods can efficiently handle, and good solutions are potentially missed. We present an alternative evolutionary method based on Genetic Algorithms and Harmony Search to accelerate clinical research and to enable the consideration of a larger number of candidate antigens during the designing of the screening. We show that compared to the traditional methodology employed by clinicians, our approach is able to produce better results in a timely manner.

Aggregation operators are mathematical functions that enable the fusion of information from multiple sources. Fuzzy Integrals (FIs) are widely used aggregation operators, which combine information in respect to a Fuzzy Measure (FM) which captures the worth of both the individual sources and all their possible combinations. However, FIs suffer from the potential drawback of not fusing information according to the intuitively interpretable FM, leading to non-intuitive results. The latter is particularly relevant when a FM has been defined using external information (e.g. experts). In order to address this and provide an alternative to the FI, the Recursive Average (RAV) aggregation operator was recently proposed which enables intuitive data fusion in respect to a given FM. With an alternative fusion operator in place, in this paper, we define the concept of `A Priori' FMs which are generated based on external information (e.g. classification accuracy) and thus provide an alternative to the traditional approaches of learning or manually specifying FMs. We proceed to develop one specific instance of such an a priori FM to support the decision level fusion step in ensemble classification. We evaluate the resulting approach by contrasting the performance of the ensemble classifiers for different FMs, including the recently introduced Uriz and the Sugeno λ-measure; as well as by employing both the Choquet FI and the RAV as possible fusion operators. Results are presented for 20 datasets from machine learning repositories and contextualised to the wider literature by comparing them to state-of-the-art ensemble classifiers such as Adaboost, Bagging, Random Forest and Majority Voting.

Constrained type-2 fuzzy sets have been proposed as a tool to model type-2 fuzzy sets starting from a type-1 generator set with uncertainty. This constrained representation only defines as acceptable the embedded sets that have the same shape as the generator set in order to process only membership functions that are considered "meaningful" when using fuzzy operators such as centroid defuzzification. However, the idea of "meaningfulness" has never been clearly defined; at the same time there are some contexts in which a given concept (e.g. medium height) can be reasonably represented by multiple shapes, such as triangular and Gaussian. The aim of this paper is both to formally define the idea of meaningfulness of shapes and to extend the formal definitions of constrained interval type-2 fuzzy sets in order to allow the presence of multiple shapes among the acceptable embedded sets.

Most real-world environments are subject to different sources of uncertainty which may vary in magnitude over time. We propose that while Type-1 (T1) Non-Singleton Fuzzy Logic System (NSFLSs) have the potential to tackle uncertainty within the input Fuzzy Sets (FSs), Type-2 (T2) input FSs provide the ability to also capture variation in uncertainty levels by means of their extra degrees of freedom. Specifically, in this paper, we propose a strategy to design Interval Type-2 (IT2) input Membership Functions (MFs) in an online manner to ensure the parameters of input MFs are updated dynamically, thus capturing varying levels of uncertainty affecting systems' inputs. In this strategy, first, uncertainty detection is performed over a given time-frame (the Uncertainty Estimation Time-frame) and Type-1 (T1) input MFs are constructed by utilising the detected uncertainty level. Second, the variation of the uncertainty levels over a sliding window (the Uncertainty Variation Window) is used to capture the degree of variation in the detected uncertainty levels over time, which in turn informs the size of the Footprint of Uncertainty (FOU) of the IT2 MF associated with the T1 principal MF. Using time-series prediction experiments as an initial evaluation and demonstration platform for the proposed architecture, we show that the proposed strategy of designing IT2 input MFs has the potential to deliver performance benefits. Specifically, it allows systems to not only adapt to specific uncertainty levels but also to be more resilient to the variation of said uncertainty levels over time, thus offering a pathway to robust performance in real-world applications.

Hierarchical fuzzy systems (HFSs) have been seen as an effective approach to reduce the complexity of fuzzy logic systems (FLSs), largely as a result of reducing the number of rules. However, it is not clear completely how complexity of HFSs can be measured. In FLSs, complexity is commonly expressed using a multi-factorial approach, taking into consideration the number of rules, variables, and fuzzy terms. However, this may not be the best way to assess complexity in HFSs that have structures involving multiple subsystems, layers and different topologies. Thus far, structural complexity associated with the structure of HFSs has not been discussed. In the field of software engineering (SE), a complexity measure has been proposed to measure program complexity. This measure uses the concept of graph theory complexity, which considers the control structure complexity. The measure can also be applied to assess the complexity of a collection of programs known as a hierarchical nest. In this paper, we present an approach to mapping an SE complexity measure to HFS design. The approach includes several mapping alternatives that are outlined and illustrated using different HFS designs. This study contributes a new approach for the first time to assessing structural complexity in HFSs based on an approach from SE complexity measure.

In this paper, we propose a novel weighted combination feature selection method using bootstrap and fuzzy sets. The proposed method mainly consists of three processes, including fuzzy sets generation using bootstrap, weighted combination of fuzzy sets and feature ranking based on defuzzification. We implemented the proposed method by combining four state-of-the-art feature selection methods and evaluated the performance based on three publicly available biomedical datasets using fivefold cross validation. Based on the feature selection results, our proposed method produced comparable (if not better) classification accuracies to the best of the individual feature selection methods for all evaluated datasets. More importantly, we also applied standard deviation and Pearson's correlation to measure the stability of the methods. Remarkably, our combination method achieved significantly higher stability than the four individual methods when variations and size reductions were introduced to the datasets.

Although driving behavior has been largely studied amongst private motor vehicles drivers, the literature addressing heavy goods vehicle (HGV) drivers is scarce. Identifying the existing groups of driving stereotypes and their proportions enables researchers, companies, and policy makers to establish group-specific strategies to improve safety and economy. In addition, insight into driving styles can help predict drivers' reactions and therefore enable the modeling of interactions between vehicles and the possible obstacles encountered on a journey. Consequently, there are also contributions to the research and development of autonomous vehicles and smart roads. In this paper, our interest lies in investigating driving behavior within the HGV community in the United Kingdom (U.K.). We conduct analysis of a telematics dataset containing the incident information on 21 193 HGV drivers across the U.K. We are interested in answering two research questions: 1) What groups of behavior are we able to uncover? 2) How do these groups complement current findings in the literature? To answer these questions, we apply a two-stage data analysis methodology involving consensus clustering and ensemble classification to the dataset. Through the analysis, eight patterns of behavior are uncovered. It is also observed that although our findings have similarities to those from previous work on driving behavior, further knowledge is obtained, such as extra patterns and driving traits arising from vehicle and road characteristics.

One of the methods for stratifying different molecular classes of breast cancer is the Nottingham prognostic index plus, which uses breast cancer relevant biomarkers to stain tumor tissues prepared on tissue microarray (TMA). To determine the molecular class of the tumor, pathologists will have to manually mark the nuclei activity biomarkers through a microscope and use a semi-quantitative assessment method to assign a histochemical score (H-Score) to each TMA core. Manually marking positively stained nuclei is a time-consuming, imprecise, and subjective process, which will lead to inter-observer and intra-observer discrepancies. In this paper, we present an end-to-end deep learning system, which directly predicts the H-Score automatically. Our system imitates the pathologists' decision process and uses one fully convolutional network (FCN) to extract all nuclei region (tumor and non-tumor), a second FCN to extract tumor nuclei region, and a multi-column convolutional neural network, which takes the outputs of the first two FCNs and the stain intensity description image as an input and acts as the high-level decision making mechanism to directly output the H-Score of the input TMA image. To the best of our knowledge, this is the first end-to-end system that takes a TMA image as the input and directly outputs a clinical score. We will present experimental results, which demonstrate that the H-Scores predicted by our model have very high and statistically significant correlation with experienced pathologists' scores and that the H-Score discrepancy between our algorithm and the pathologists is on par with the inter-subject discrepancy between the pathologists.

Fuzzy logic has been widely used to model human reasoning thanks to its inherent capability of handling uncertainty. In particular, the introduction of Type-2 fuzzy sets added the possibility of expressing uncertainty even on the definition of the membership functions. Type-2 sets, however, don’t pose any restrictions on the continuity or convexity of their embedded sets while these properties may be desirable in certain contexts. To overcome this problem, Constrained Type-2 fuzzy sets have been proposed. In this paper, we focus on Interval Constrained Type-2 sets to see how their unique structure can be exploited to build a new inference process. This will set some ground work for future developments, such as the design of a new defuzzification process for Constrained Type-2 fuzzy systems.

Real world environments face a wide range of sources of noise and uncertainty. Thus, the ability to handle various uncertainties, including noise, becomes an indispensable element of automated decision making. Non-Singleton Fuzzy Logic Systems (NSFLSs) have the potential to tackle uncertainty within the design of fuzzy systems. The firing strength has a significant role in the accuracy of FLSs, being based on the interaction of the input and antecedent fuzzy sets. Recent studies have shown that the standard technique for determining firing strengths risks substantial information loss in terms of the interaction of the input and antecedents. Recently, this issue has been addressed through exploration of alternative approaches which employ the centroid of the intersection (cen-NS) and the similarity (sim-NS) between input and antecedent fuzzy sets. This paper identifies potential shortcomings in respect to the previously introduced similarity-based NSFLSs in which firing strength is defined as the similarity between an input FS and an antecedent. To address these shortcomings, this paper explores the potential of the subsethood measure to generate a more suitable firing level (sub-NS) in NSFLSs featuring various noise levels. In the experiment, the basic waiter tipping fuzzy logic system is used to examine the behaviour ofsub-NS in comparison with the current approaches. Analysis of the results shows that thesub-NS approach can lead to more stable behaviour in real world applications.

Real-world environments face a wide range of noise (uncertainty) sources and gaining insight into the level of noise is a critical part of many applications. While Non-Singleton Fuzzy Logic Systems (NSFLSs), in particular recently introduced advanced variants such as centroid-based NSFLSs have the capacity to handle known quantities of uncertainty, thus far, the actual level of uncertainty has had to be defined a priori - i.e. prior to run time of a system or controller. This paper does not focus on such advances within the architecture of NSFLSs, but focuses on a novel two-stage approach for uncertainty handling in fuzzy logic systems which integrates: (i) estimation of noise levels and (ii) the appropriate handling of the noise based on this estimate, by means of a dynamically configured NSFLS. As initial evaluation of the approach, two chaotic nonlinear time series (Mackey-Glass and Lorenz), as well as a real-world Darwin sea level pressure series prediction fuzzy logic systems are implemented and compared to commonly used procedures. The results indicate that the proposed strategy of integrating uncertainty/noise estimation with the capacity of non-singleton fuzzy logic systems has the potential to deliver performance benefits in real-world applications without requiring a priori information on noise levels and thus delivers a first step towards smart, noise-adaptive non-singleton fuzzy logic systems and controllers.

© 2018 IEEE. In this paper, based on a fuzzy entropy feature selection framework, different methods have been implemented and compared to improve the key components of the framework. Those methods include the combinations of three ideal vector calculations, three maximal similarity classifiers and three fuzzy entropy functions. Different feature removal orders based on the fuzzy entropy values were also compared. The proposed method was evaluated on three publicly available biomedical datasets, including Wisconsin Breast Cancer(WBC), Wisconsin Diagnostic Breast Cancer(WDBC) and Parkinsons. From the experiments, we concluded the optimized combination of the ideal vector, similarity classifier and fuzzy entropy function for feature selection. The optimized framework was also compared with other six classical filter-based feature selection methods. The proposed method was ranked as one of the top performers together with the Correlation and ReliefF methods. The proposed method achieved classification accuracies of 96.97%, 94.85% and 78.23% for the WBC, WDBC and Parkinsons datasets respectively. More importantly, the proposed method achieved the most stable performance for all three datasets when the features being gradually removed. This indicates a better feature ranking performance than the other compared methods.

We take advantage of the popularity of deep convolutional neural networks (CNNs) and have developed a very simple image quality assessment method that rivals state of the art. We show that convolutional layer outputs (deep features) of a CNN compute the local structural information of spatial regions of different sizes in the input image. The learned convolutional kernels contain a much richer set of weights thus capturing much more local structural information than hand crafted ones. As the deep features learned from large datasets already contain very rich multi-resolutional structural image information, they can be directly used to calculate visual distortion of an image and it is not necessary to introduce further complicated computational process. We will present experimental results to demonstrate that this is indeed the case, and that simple cosine distance of the deep features is as good as state the art methods for full reference image quality assessment.

Presents a brief historical review of the various Editors in Chief of the IEEE Transactions on Fuzzy Systems.

The Karnik-Mendel algorithm is used to compute the centroid of interval type-2 fuzzy sets, determining the switch points needed for the lower and upper bounds of the centroid, through an iterative process. It is commonly acknowledged that there is no closed-form solution for determining such switch points. Many enhanced algorithms have been proposed to improve the computational efficiency of the Karnik-Mendel algorithm. However, all of these algorithms are still based on iterative procedures. In this paper, a direct approach based on derivatives for determining the switch points without multiple iterations has been proposed, together with mathematical proof that these switch points are correctly determining the lower and upper bounds of the centroid. Experimental simulations show that the direct approach obtains the same switch points, but is more computationally efficient than any of the existing (iterative) algorithms. Thus, we propose that this algorithm should be used in any application of interval type-2 fuzzy sets in which the centroid is required.

This letter is a supplement to the previous paper “A Direct Approach for Determining the Switch Points in the Karnik-Mendel Algorithm”. In the previous paper, the enhanced iterative algorithm with stop condition (EIASC) was shown to be the most inefficient in R. Such outcome is apparently different from the results in another paper in which EIASC was illustrated to be the most efficient in MATLAB. An investigation has been made into this apparent inconsistency and it can be confirmed that both the results in R and MATLAB are valid for the EIASC algorithm. The main reason for such phenomenon is the efficiency difference of loop operations in R and MATLAB. It should be noted that the efficiency of an algorithm is closely related to its implementation in practice. In this letter, we update the comparisons of the three algorithms in the previous paper, based on optimized implementations under five programming languages (MATLAB, R, Python, C, and Java). From this, we conclude that results in one programming language cannot be simply extended to all languages.

In a previous paper, we proposed an extended ANFIS architecture and showed that interval type-2 ANFIS produced larger errors than type-1 ANFIS on the well-known IRIS classification problem. In this paper, more experiments on both synthetic and real-world data are conducted to further investigate and compare the performance of interval type-2 ANFIS and type-1 ANFIS. For each dataset, interval type-2 ANFIS is optimised in three different ways, including a strategy suggested by Mendel such that interval type-2 ANFIS would be no worse than type-1 ANFIS. Our results show that in some circumstances the performance of interval type-2 ANFIS can be improved when it is initialised with blurred optimised type-1 ANFIS parameters. However, in general, interval type-2 ANFIS does not produce a clear performance improvement compared to type-1 ANFIS, especially on Mackey-Glass data with large noise. Thus, we conclude that the choice of interval type-2 ANFIS over type-1 ANFIS should be carefully considered, since type-2 ANFIS is more computationally complex, yet significantly better performance cannot be easily obtained.

As non-singleton fuzzy logic controllers (NSFLCs) are capable of capturing input uncertainties, they have been effectively used to control and navigate unmanned aerial vehicles (UAVs) recently. To further enhance the capability to handle the input uncertainty for the UAV applications, a novel NSFLC with the recently introduced similarity-based inference engine, i.e., Sim-NSFLC, is developed. In this paper, a comparative study in a 3D trajectory tracking application has been carried out using the aforementioned Sim-NSFLC and the NSFLCs with the standard as well as centroid composition-based inference engines, i.e., Sta-NSFLC and Cen-NSFLC. All the NSFLCs are developed within the robot operating system (ROS) using the C++ programming language. Extensive ROS Gazebo simulation-based experiments show that the Sim-NSFLCs can achieve better control performance for the UAVs in comparison with the Sta-NSFLCs and Cen-NSFLCs under different input noise levels.

Multi-criteria decision making (MCDM) problems are a well known category of decision making problem that has received much attention in the literature, with a key approach being the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). While TOPSIS has been developed towards the use of Type-2 Fuzzy Sets (T2FS), to date, the additional information provided by T2FSs in TOPSIS has been largely Ignored since the final output, the Closeness Coefficient (CC), has remained a crisp value. In this paper, we develop an alternative approach to T2 fuzzy TOPSIS, where the final CC values adopt an interval-valued form. We show in a series of systematically designed experiments, how increasing uncertainty in the T2 membership functions affects the interval-valued CC outputs. Specifically, we highlight the complex behaviour in terms of the relationship of the uncertainty levels and the outputs, including non-symmetric and non-linear growth in the CC intervals in response to linearly growing levels of uncertainty. As the first TOPSIS approach which provides an interval-valued output to capture output uncertainty, the proposed method is designed to reduce the loss of information and to maximize the benefit of using T2FSs. The initial results indicate substantial potential in the further development and exploration of the proposed and similar approaches and the paper highlights promising next steps.

Non-singleton fuzzification is used to model uncertain (e.g. noisy) inputs within fuzzy logic systems. In the standard approach, assuming the fuzzification type is known, the observed [noisy] input is usually considered to be the core of the input fuzzy set, usually being the centre of its membership function. This paper proposes a new fuzzification method (not type), in which the core of an input fuzzy set is not necessarily located at the observed input, rather it is dynamically adjusted based on statistical methods. Using the weighted moving average, a few past samples are aggregated to roughly estimate where the input fuzzy set should be located. While the added complexity is not huge, applying this method to the well-known Mackey-Glass and Lorenz time-series prediction problems, show significant error reduction when the input is corrupted by different noise levels.

Hierarchical fuzzy systems (HFSs) have been shown to have the potential to improve interpretability of fuzzy logic systems (FLSs). In recent years, a variety of indices have been proposed to measure the interpretability of FLSs such as the Nauck index and Fuzzy index. However, interpretability indices associated with HFSs have not so far been discussed. The structure of HFSs, with multiple layers, subsystems, and varied topologies, is the main challenge in constructing interpretability indices for HFSs. Thus, the comparison of interpretability between FLSs and HFSs-even at the index level-is still subject to open discussion. This paper begins to address these challenges by introducing extensions to the FLS Nauck and Fuzzy interpretability indices for HFSs. Using the proposed indices, we explore the concept of interpretability in relation to the different structures in FLSs and HFSs. Initial experiments on benchmark datasets show that based on the proposed indices, HFSs with equivalent function to FLSs produce higher indices, i.e. are more interpretable than their corresponding FLSs.

Non-Singleton Fuzzy Logic Systems (NSFLSs) have the potential to tackle uncertainty within the design of fuzzy systems. The inference process has a major role in determining results, being partly based on the interaction of input and antecedent fuzzy sets (in generating firing levels). Recent studies have shown that the standard technique for determining firing strengths risks substantial information loss in terms of the interaction of the input and antecedents. To address this issue, alternative approaches, which employ the centroid of intersections (cen-NS) and similarity measures (sim-NS), have been developed. More recently, a novel similarity measure for fuzzy sets has been introduced, but as yet this has not been used for NSFLSs. This paper focuses on exploring the potential of this new similarity measure in combination with the sim-NS approach to generate a more suitable firing level for non-singleton input. Experiments are presented for fuzzy systems trained using both noisy and noise-free time series. The prediction results of NSFLSs for the novel similarity measure and the current approaches are compared. Analysis of the results shows that the novel similarity measure, used within the sim-NS approach, can be a more stable and suitable method suitable to be used in real world applications.

Most applications of both type-1 and type-2 fuzzy logic systems are employing singleton fuzzification due to its simplicity and reduction in its computational speed. However, using singleton fuzzification assumes that the input data (i.e., measurements) are precise with no uncertainty associated with them. This paper explores the potential of combining the uncertainty modelling capacity of interval type-2 fuzzy sets with the simplicity of type-1 fuzzy logic systems (FLSs) by using interval type-2 fuzzy sets solely as part of the non-singleton input fuzzifier. This paper builds on previous work and uses the methodological design of the footprint of uncertainty (FOU) of interval type-2 fuzzy sets for given levels of uncertainty. We provide a detailed investigation into the ability of both types of fuzzy sets (type-1 and interval type-2) to capture and model different levels of uncertainty/noise through varying the size of the FOU of the underlying input fuzzy sets from type-1 fuzzy sets to very “wide” interval type-2 fuzzy sets as part of type-1 non-singleton FLSs using interval type-2 input fuzzy sets. By applying the study in the context of chaotic time-series prediction, we show how, as uncertainty/noise increases, interval type-2 input fuzzy sets with FOUs of increasing size become more and more viable.

In this paper, an extended ANFIS architecture is proposed. By incorporating an extra layer for the fuzzification process, the extended architecture is able to fit both type-1 and interval type-2 models. The learning properties of the proposed architecture based on the least-squares estimate method are studied on selected type-1 and interval type-2 ANFIS models. We show that the least-squares estimate method in general behaves differently for interval type-2 ANFIS models compared to type-1 ANFIS models, producing larger errors for interval type-2 ANFIS.

Fuzzy logic controllers (FLCs) have extensively been used for the autonomous control and guidance of unmanned aerial vehicles (UAVs) due to their capability of handling uncertainties and delivering adequate control without the need for a precise, mathematical system model which is often either unavailable or highly costly to develop. Despite the fact that non-singleton FLCs (NSFLCs) have shown more promising performance in several applications when compared to their singleton counterparts (SFLCs), most of UAV applications are still realized by using SFLCs. In this paper, we explore the potential of both standard and the recently introduced centroid based NSFLCs, i.e., Sta-NSFLC and Cen-NSFLC, for the control of a quadcopter UAV under various input noise conditions using different levels of fuzzifier, and a comparative study has been conducted using the three aforementioned FLCs. We present a series of simulation-based experiments, the simulation results show that the control performances of NSFLCs are better than those of SFLC, and the Cen-NSFLC outperforms the Sta-NSFLC especially under highly noisy conditions.

Multi Criteria Decision Making is a challenging but vital process for organizations. One of the best-known techniques to support Multi-Criteria Decision Making is the `Technique for Order Preference by Similarity to Ideal Solution' (TOPSIS) approach. In recent years, a variety of extensions, including fuzzy extensions of TOPSIS have been proposed. Besides the many variations of standard TOPSIS, one family of extensions employing fuzzy sets is referred to as fuzzy TOPSIS (FTOPSIS). One challenge that has arisen is that it is not straightforward to choose between the multiple variants of TOPSIS existing today. Previously, none of the papers that have compared the key differences between standard and fuzzy TOPSIS have fully explored each of the step-wise stages. In this paper, we now provide a detailed comparison of these key stages in a systematic stepwise manner, clearly highlighting differences. We also identify and discuss the limitations, issues and challenges which exist in the present FTOPSIS method. The crucial and main issues are identified as relating to concepts of reliability, truth and meaning. Having identified these conceptual issues, we then go on to highlight what we argue to be the main issue, that of reliability, to discuss further. We proceed to present a potential solution and propose a framework to address the issue. This study will provide guidelines to researchers in this field and to provide potential pathways to further solutions, which have the capacity to advance the area of FTOPSIS as a whole.

In non-singleton fuzzy logic systems (NSFLSs) input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty such as sensor noise. The performance of NSFLSs in handling such uncertainties depends both on the actual input fuzzy sets (and their inherent model of uncertainty) and on the way that they affect the inference process. This paper proposes a novel type of NSFLS by replacing the composition-based inference method of type-1 fuzzy relations with a similarity-based inference method that makes NSFLSs more sensitive to changes in the input's uncertainty characteristics. The proposed approach is based on using the Jaccard ratio to measure the similarity between input and antecedent fuzzy sets, then using the measured similarity to determine the firing strength of each individual fuzzy rule. The standard and novel approaches to NSFLSs are experimentally compared for the well-known problem of Mackey-Glass time series predictions, where the NSFLS's inputs have been perturbed with different levels of Gaussian noise. The experiments are repeated for system training under both noisy and noise-free conditions. Analyses of the results show that the new method outperforms the standard approach by substantially reducing the prediction errors.

Recent studies in breast cancer domains have identified seven distinct clinical phenotypes (groups) using immunohistochemical analysis and a variety of unsupervised learning techniques. Consensus among the clustering algorithms has been used to categorise patients into these specific groups, but often at the expenses of not classifying all patients. It is known that fuzzy methodologies can provide linguistic based classification rules to ease those from consensus clustering. The objective of this study is to present the validation of a recently developed extension of a fuzzy quantification subsethood-based algorithm on three sets of newly available breast cancer data. Results show that our algorithm is able to reproduce the seven biological classes previously identified, preserving their characterisation in terms of marker distributions and therefore their clinical meaning. Moreover, because our algorithm constitutes the fundamental basis of the newly developed Nottingham Prognostic Index Plus (NPI+), our findings demonstrate that this new medical decision making tool can help moving towards a more tailored care in breast cancer.

In nonsingleton fuzzy logic systems (NSFLSs), input uncertainties are modeled with input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of NSFLSs in handling such uncertainties depends on both the appropriate modeling in the input fuzzy sets of the uncertainties present in the system's inputs and on how the input fuzzy sets (and their inherent model of uncertainty) interact with the antecedent and, thus, affect the inference within the remainder of the NSFLS. This paper proposes a novel development on the latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is proposed and applied to build a new type of NSFLS. The proposed approach is based on employing the centroid of the intersection of input and antecedent sets as origin of the firing degree, rather than the traditional maximum of their intersection, thus making the NSFLS more sensitive to changes in the input's uncertainty characteristics. The traditional and novel approach to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and Lorenz chaotic time-series predictions, where the NSFLSs' inputs have been perturbed with different levels of Gaussian noise. Experiments are repeated for system training under noisy and noise-free conditions. Analyses of the results show that the new method outperforms the traditional approach. Moreover, it is shown that while formally more complex, in practice, the new method has no significant computational overhead compared with the standard approach.

Capturing the uncertainty arising from system noise has been a core feature of fuzzy logic systems (FLSs) for many years. This paper builds on previous work and explores the methodological transition of type-1 (T1) to interval type-2 fuzzy sets (IT2 FSs) for given “levels” of uncertainty. Specifically, we propose to transition from T1 to IT2 FLSs through varying the size of the Footprint Of Uncertainty (FOU) of their respective FSs while maintaining the original FS shape (e.g., triangular) and keeping the size of the FOU over the FS as constant as possible. The latter is important as it enables the systematic relating of FOU size to levels of uncertainty and vice versa, while the former enables an intuitive comparison between the T1 and T2 FSs. The effectiveness of the proposed method is demonstrated through a series of experiments using the well-known Mackey-Glass (MG) time series prediction problem. The results are compared with the results of the IT2 FS creation method introduced in [1] which follows a similar methodology as the proposed approach but does not maintain the membership function (MF) shape.

The rationale behind ensemble machine learning systems is the creation of many classifiers and the combination of their output such that the combination improves the performance of each single classifier. There are two key issues in the creation of ensemble classifiers: one is how two select and group the data samples to train the individual models and the other is how to select or combine the multiple outputs.

The main feature of type-2 fuzzy sets is their ability to represent uncertainties within a system. These uncertainties are captured in the Footprint Of Uncertainty (FOU) of a type2 membership function which can be described by the upper and the lower membership function. One of the challenges in modelling a type-2 fuzzy logic system is the problem of defining the membership function parameters and their FOUs, given noisy data or imperfect measurements. This challenge is increased by the complexity which arises from the increase in the number of parameters of IT2 MFs to be tuned. This paper presents a novel method for designing interval type-2 fuzzy logic systems, in which the FOU creation method presented in [1] is adopted, and then the design parameters are tuned through simulated annealing. The novelty of this approach is that it has fewer parameters to be tuned than the conventional approach, as only a single extra parameter is used to define the IT2 MFs. We demonstrate the approach through application to the Mackey-Glass time series prediction problem, using training data sets corrupted with different levels of noise. By doing so, we demonstrate that this approach is an efficient FOU selection mechanism that produces IT2 FLSs with good performance using less computational time than the conventional approach.

Multi Criteria Decision Making methods have been developed to solve complex real-world decision problems. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is currently one of the most popular methods and has been shown to provide helpful outputs in various application areas. In recent years, a variety of extensions, including fuzzy extensions of TOPSIS have been proposed. One challenge that has arisen is that it is not straightforward to differentiate between the multiple variants of TOPSIS existing today. Thus, in this paper, a comparison between the classical Fuzzy TOPSIS method proposed by Chen in 2000 and the recently Fuzzy TOPSIS proposed extension by Yuen in 2014 is made. The purpose of this comparative study is to show the difference between both methods and to provide context for their respective strengths and limitations both in complexity of application, and expressiveness of results. A detailed synthetic numeric example and comparison of both methods are provided.

Big longitudinal observational medical data potentially hold a wealth of information and have been recognised as potential sources for gaining new drug safety knowledge. Unfortunately there are many complexities and underlying issues when analysing longitudinal observational data. Due to these complexities, existing methods for large-scale detection of negative side effects using observational data all tend to have issues distinguishing between association and causality. New methods that can better discriminate causal and non-causal relationships need to be developed to fully utilise the data. In this paper we propose using a set of causality considerations developed by the epidemiologist Bradford Hill as a basis for engineering features that enable the application of supervised learning for the problem of detecting negative side effects. The Bradford Hill considerations look at various perspectives of a drug and outcome relationship to determine whether it shows causal traits. We taught a classifier to find patterns within these perspectives and it learned to discriminate between association and causality. The novelty of this research is the combination of supervised learning and Bradford Hill's causality considerations to automate the Bradford Hill's causality assessment. We evaluated the framework on a drug safety gold standard known as the observational medical outcomes partnership's non-specified association reference set. The methodology obtained excellent discrimination ability with area under the curves ranging between 0.792 and 0.940 (existing method optimal: 0.73) and a mean average precision of 0.640 (existing method optimal: 0.141). The proposed features can be calculated efficiently and be readily updated, making the framework suitable for big observational data.

This paper presents a natural language processing (NLP) system that was designed to participate in the 2014 i2b2 de-identification challenge. The challenge task aims to identify and classify seven main Protected Health Information (PHI) categories and 25 associated sub-categories. A hybrid model was proposed which combines machine learning techniques with keyword-based and rule-based approaches to deal with the complexity inherent in PHI categories. Our proposed approaches exploit a rich set of linguistic features, both syntactic and word surface-oriented, which are further enriched by task-specific features and regular expression template patterns to characterize the semantics of various PHI categories. Our system achieved promising accuracy on the challenge test data with an overall micro-averaged F-measure of 93.6%, which was the winner of this de-identification challenge.

• Risk factor detection is of great importance for the treatment of heart disease. • Machine learning techniques combined with keywords and rule-based approaches. • 7 main heart disease risk factors with relevant medications are identified. • Achieving an overall micro-averaged F -measure of 91.56%. Coronary artery disease (CAD) is the leading cause of death in both the UK and worldwide. The detection of related risk factors and tracking their progress over time is of great importance for early prevention and treatment of CAD. This paper describes an information extraction system that was developed to automatically identify risk factors for heart disease in medical records while the authors participated in the 2014 i2b2/UTHealth NLP Challenge. Our approaches rely on several nature language processing (NLP) techniques such as machine learning, rule-based methods, and dictionary-based keyword spotting to cope with complicated clinical contexts inherent in a wide variety of risk factors. Our system achieved encouraging performance on the challenge test data with an overall micro-averaged F -measure of 0.915, which was competitive to the best system ( F -measure of 0.927) of this challenge task.

In this paper, a new approach is presented to model interval-based data using fuzzy sets (FSs). Specifically, we show how both crisp and uncertain intervals (where there is uncertainty about the endpoints of intervals) collected from individual or multiple survey participants over single or repeated surveys can be modeled using type-1, interval type-2, or general type-2 FSs based on zSlices. The proposed approach is designed to minimize any loss of information when transferring the interval-based data into FS models, and to avoid, as much as possible, assumptions about the distribution of the data. Furthermore, our approach does not rely on data preprocessing or outlier removal, which can lead to the elimination of important information. Different types of uncertainty contained within the data, namely intra- and inter-source uncertainty, are identified and modeled using the different degrees of freedom of type-2 FSs, thus providing a clear representation and separation of these individual types of uncertainty present in the data. We provide full details of the proposed approach, as well as a series of detailed examples based on both real-world and synthetic data. We perform comparisons with analogue techniques to derive FSs from intervals, namely the interval approach and the enhanced interval approach, and highlight the practical applicability of the proposed approach.

In previous work, a novel supervised framework implementing a binary classifier was presented that obtained excellent results for side effect discovery. Interestingly, unique side effects were identified when different binary classifiers were used within the framework, prompting the investigation of applying a multiple classifier system. In this paper we investigate tuning a side effect multiple classifying system using genetic algorithms. The results of this research show that the novel framework implementing a multiple classifying system trained using genetic algorithms can obtain a higher partial area under the receiver operating characteristic curve than implementing a single classifier. Furthermore, the framework is able to detect side effects efficiently and obtains a low false positive rate.

A recurring theme in research employing type-2 fuzzy sets is the question of how much uncertainty in a given context warrants the application of type-2 fuzzy sets and systems over their type-1 counterparts. In this paper we provide insight into this challenging question through a detailed investigation into the ability of both types of Fuzzy Logic Systems (FLSs) to capture and model different levels of uncertainty/noise through varying the size of the Footprint Of Uncertainty (FOU) of the underlying fuzzy sets from type-1 fuzzy sets to very "wide" interval type-2 fuzzy sets. By applying the study in the well-controlled context of chaotic time-series prediction, we show how, as uncertainty/noise increases, type-2 FLSs with fuzzy sets with FOUs of increasing size become more and more viable. While the work in this paper is focused on a specific application, we believe it provides crucial insight into the challenging question of the viability of interval type-2 over type-1 FLSs.

In this paper, we present a complete inferencing framework based on L-fuzzy sets, comprising fuzzification, inferencing itself, and both linguistic and numeric defuzzification strategies. We present the algorithms for each step, and then present a range of worked examples to illustrate the methods. Finally, we compare the results with similar examples which carry out `standard' Mandani-style inference. To the best of our knowledge, this is the first time that practical algorithms for complete L-fuzzy inference have been presented.

The idea behind distance metric learning (DML) is to accentuate the distance relations found in the training data, maintaining whether the data patterns are similar or dissimilar. In this paper, we investigate in using DML (GDML, LMNN, MCML and NCA) in semi-supervised Fuzzy c-means clustering and apply them on a real, biomedical dataset and on UCI datasets. We used a cross validation setting with varying amount of labelled data to test our methodology. Out of eight datasets, statistical significant improvement was found on five datasets using ssFCM with DML. This shows that DML can improve ssFCM clustering for some datasets. Further analysis using 2D PCA projection and sum of squared distances before and after DML transformation of the original data are carried out. Interestingly, DML was found to worsen ssFCM clustering in the NTBC dataset with hierarchical clusters.

In this paper we explore the characteristics of Type-1 Fuzzy Set agreement models based on interval data through contrasting statistical measures of the fuzzy models and the raw data respectively. We create Type-1 Fuzzy Set models using the Interval Agreement Approach, and then extract a preliminary set of attributes that encapsulate aspects of the agreement models. In order to explore what these attributes can tell us, we compare them with a set of traditional statistical measures of consensus which are applied to the raw data. Two interval-valued survey data sets are employed in this study, a synthetic data set consisting of 30 groups of 10 experts rating 25 objects which is used to provide a large example, and a real-world data set consisting of 7 groups of 4-8 cyber-security experts rating 26 security components that was collected during a decision making exercise at GCHQ, Cheltenham, UK. We show that while there are areas in which traditional methods and the attributes extracted from the Type-1 Fuzzy Set agreement models overlap, there are also attributes that do not appear to be replicated, suggesting that these attributes contain additional information about the consensus within the groups. A discussion of the results is provided, along with the conclusions that can be drawn and considerations for future work on this subject.

Breast cancer is one of the most frequently occurring cancers among women throughout the world. In breast cancer prognosis, grading plays an important role. In this paper, we apply a novel method based on type-II fuzzy logic to Fourier Transform Infra-red Spectroscopy based breast cancer spectral data for the classification of breast cancer grade. A FTIR spectral data set consisting of 14 cases of breast cancer has been used. A zSlices based type-II fuzzy logic approach has been used to create prototype models for the classification of unseen breast cancer cases. The prototype models are used with a similarity measure to classify unseen cases of cancer. We have shown that the T-II similarity based model is a promising methodology for classification.

In this paper an optimized AdaBoost Regression and Threshold (AdaBoostRT) algorithm based on feed-forward neural networks is evaluated. The AdaBoostRT algorithm is used to combine an ensemble of feed-forward neural networks trained by using backpropagation algorithm (FFN-BP). The ensemble model is validated by using two typical time-series data, namely Chua's circuit and CATS benchmark data. The performance of the ensemble models is shown to outperform several existing approaches.

Consumer Debt has risen to be an important problem of modern societies, generating a lot of research in order to understand the nature of consumer indebtness, which so far its modelling has been carried out by statistical models. In this work we show that Computational Intelligence can offer a more holistic approach that is more suitable for the complex relationships an indebtness dataset has and Linear Regression cannot uncover. In particular, as our results show, Neural Networks achieve the best performance in modelling consumer indebtness, especially when they manage to incorporate the significant and experimentally verified results of the Data Mining process in the model, exploiting the flexibility Neural Networks offer in designing their topology. This novel method forms an elaborate framework to model Consumer indebtness that can be extended to any other real world application.

The aim of this work is to identify clinically-useful and stable breast cancer subgroups using a reduced panel of biomarkers. First, we investigate the stability of subgroups generated using two different reduced panels of biomarkers on clustering of breast cancer data. The stability of the subgroups found are assessed based on comparison of agreement levels using Cohen's Kappa Index on clustering solutions from ssFCM methodologies, consensus K-means and model-based clustering. The clustering solutions obtained from the feature set which achieve the higher agreement is chosen for further biological and clinical evaluation to establish the subgroups are clinically-useful. Using a ssFCM methodology, we identified seven clinically-useful and stable breast cancer subgroups using a reduced panel by Soria et al. So far, the stability of the subgroups identified using the reduced panel of biomarkers have not yet been investigated.

In this paper, we introduce an implementation of a fuzzy system whose parameters are mutable according to the context. The construction of the system is done via two steps. First, we build a based type-1 Takagi-Sugeno-Kang (TSK) fuzzy system whose membership functions will be later adjusted to the situation by means of contextual transformation to reflect the influence of context in the interpretation of fuzzy sets. Second, an iterative algorithm is performed to identify the transformation matrix, which is used to scale the membership functions of the reference-based fuzzy sets in each of the contexts. The identification of the premise part of the based fuzzy system is performed via a combination of an island model parallel genetic algorithm and a space search memetic algorithm, while the identification of the consequent parameters of the system is done via an improved QR Householder least-squares method. The proposed system is evaluated using the well-known Mackey-Glass time-series prediction benchmark dataset and has shown better accuracy than any other previous works concerning the same problem.

Drugs are frequently prescribed to patients with the aim of improving each patient's medical state, but an unfortunate consequence of most prescription drugs is the occurrence of undesirable side effects. Side effects that occur in more than one in a thousand patients are likely to be signaled efficiently by current drug surveillance methods, however, these same methods may take decades before generating signals for rarer side effects, risking medical morbidity or mortality in patients prescribed the drug while the rare side effect is undiscovered. In this paper, we propose a novel computational metaanalysis framework for signaling rare side effects that integrates existing methods, knowledge from the web,metric learning, and semisupervised clustering. The novel framework was able to signal many known rare and serious side effects for the selection of drugs investigated, such as tendon rupture when prescribed Ciprofloxacin or Levofloxacin, renal failure with Naproxen and depression associated with Rimonabant. Furthermore, for the majority of the drugs investigated it generated signals for rare side effects at a more stringent signaling threshold than existing methods and shows the potential to become a fundamental part of post marketing surveillance to detect rare side effects.

Side effects of prescription drugs present a serious issue. Existing algorithms that detect side effects generally require further analysis to confirm causality. In this paper we investigate attributes based on the Bradford-Hill causality criteria that could be used by a classifying algorithm to definitively identify side effects directly. We found that it would be advantageous to use attributes based on the association strength, temporality and specificity criteria.

Designing secure software systems is a non-trivial task as data on uncommon attacks is limited, costs are difficult to estimate, and technology and tools are continually changing. Consequently, a great deal of expertise is required to assess the security risks posed to a proposed system in its design stage. In this research we demonstrate how Evolutionary Algorithms (EAs) and Simulated Annealing (SA) can be used with Ordered Weighted Average (OWA) operators to provide a suitable aggregation tool for combining experts' opinions of individual components of an specific technical attack to produce an overall rating that can be used to rank attacks in order of salience. A set of thirty nine cyber security experts took part in an exercise in which they independently assessed a realistic system scenario. We show that using EAs and SA, OWA operators can be tuned to produce aggregations that are more stable when applied to a group of experts' ratings than those produced by the arithmetic mean, and that the difference between the solutions found by each of the algorithms is minimal. However, EAs do prove to be a quicker method of search when an equivalent number of evaluations is performed by each method.

Performance measurement of robotic controllers based on fuzzy logic, operating under uncertainty, is a subject area which has been somewhat ignored in the current literature. In this paper standard measures such as RMSE are shown to be inappropriate for use under conditions where the environmental uncertainty changes significantly between experiments. An overview of current methods which have been applied by other authors is presented, followed by a design of a more sophisticated method of comparison. This method is then applied to a robotic control problem to observe its outcome compared with a single measure. Results show that the technique described provides a more robust method of performance comparison than less complex methods allowing better comparisons to be drawn.

In previous work, six clinically novel and useful subgroups of breast cancer were identified using rules and clinicians' expertise to combine solutions from three different clustering algorithms on a database of biomarkers. The motivation for the present work is to reproduce this classification using a single clustering method. In the long term, we hope to produce a clinically useful classification using fewer features (biomarkers), reducing the time and cost of running complex and expensive clinical tests. Hence, the aim of this paper is to investigate the use of feature selection in combination with ssFCM to reduce the number of features while maintaining accuracy (defined as agreement with the previous classification), both on our breast cancer biomarker data and on other benchmark datasets. We show experimental results using four feature selection techniques, exploring with 10, 15 and 17 selected features out of the original 25 biomarkers for breast cancer. We experimented with varying amounts of labelled data (10% - 60% of the training data) and we evaluate classification accuracy using cross-validation. It was found that classification accuracy increased using 15 or 17 breast cancer biomarkers. Using SVM-RFE and CFS, improved classification accuracy was found on three UCI datasets, Arrhythmia, Cardiotocography and Yeast.

This paper presents a hybrid identification method for Takagi-Sugeno-Kang (TSK) fuzzy model by means of a combination of optimisation techniques. First, the K-means clustering algorithm is used to get information granules (centres of clusters) which are used as the initial location of apexes of the MFs in the premise and the prototypes of the polynomial functions used in the consequent parts of the fuzzy rules. Subsequently, the initial fuzzy system is evolved iteratively by means of a hybrid learning. In particular, the premise part parameters are tuned by a combination of a Island Model Parallel Genetic Algorithm (IMPGA) and a space search Memetic Algorithm (MA) while the consequent parameters of the system are derived optimally by an improved QR Householder least square method (LSM). The optimisation search algorithm (IMPGA+MA) allows exploring the search space in multiple trajectories simultaneously to avoid getting trapped in local-optimal while the improved LSM helps minimize the occurrences of the underflow and overflow problems when dealing with floating point numbers. The proposed optimisation framework can be applied for a variety of application areas such as function approximation, time-series prediction, etc. However, in this paper, the proposed method is only evaluated using the well-known Mackey-Glass time-series prediction benchmark and has shown a better prediction accuracy than any other previous works of the same problem.

Non-stationary fuzzy sets have been introduced to model variation in human reasoning. While they have some similarities to type-2 fuzzy sets, there are many detailed differences. One of these differences is that they may feature horizontal random perturbations of membership functions, which result in distributions across the membership grades over time, termed temporal membership grades, which are somewhat akin to secondary membership grades of type-2 fuzzy sets. In this paper we study the distribution of the temporal membership grades of non-stationary fuzzy sets with Gaussian underlying membership functions. We derive the distribution of these grades when the non-stationary fuzzy sets are obtained by variations in location using a normal distribution. We show how to estimate the parameters of the derived distribution using numerical optimisation. In addition, we investigate the changes in the distributions obtained when using variations in location using a uniform distribution. Finally, we exhibit the performance of the beta and logistic normal distribution using examples of simulated data. In doing so, we further explore the relationships between non-stationary and type-2 fuzzy sets.

In this paper we explore the practical application of the previously introduced approach [1] to generate fuzzy sets from interval-valued data. We demonstrate two specific example applications where we 1) generate type-1 fuzzy sets from interval-valued survey data for both words (e.g., neutral, excellent) and concepts (e.g., ambience, food) and 2) generate zSlices based general type-2 fuzzy set valued data from multiple iterations of a survey. We highlight the need for the simultaneous rating of both concepts and words in order to maintain context (including timeliness) of the resulting models. Further, in both example applications, we demonstrate using the Jaccard similarity measure how similarity measures can be employed to both relate and attribute word models to concept models (e.g., excellent food) and compare different concepts directly for different contexts (e.g., ambience in venue A vs. ambience in venue B). We provide interpretations for the resulting word/concept models and similarity values and highlight their utility, for example, for the data-driven generation of linguistic descriptions of venues. Finally, we highlight remaining questions and challenges both in technical terms and in application terms.

In this paper, we propose a multi-restart memetic algorithm framework for box constrained global continuous optimisation. In this framework, an evolutionary algorithm (EA) and a local optimizer are employed as separated building blocks. The EA is used to explore the search space for very promising solutions (e.g., solutions in the attraction basin of the global optimum) through its exploration capability and previous EA search history, and local search is used to improve these promising solutions to local optima. An estimation of distribution algorithm (EDA) combined with a derivative free local optimizer, called NEWUOA (M. Powell, Developments of NEWUOA for minimization without derivatives. Journal of Numerical Analysis, 28:649-664, 2008), is developed based on this framework and empirically compared with several well-known EAs on a set of 40 commonly used test functions. The main components of the specific algorithm include: (1) an adaptive multivariate probability model, (2) a multiple sampling strategy, (3) decoupling of the hybridisation strategy, and (4) a restart mechanism. The adaptive multivariate probability model and multiple sampling strategy are designed to enhance the exploration capability. The restart mechanism attempts to make the search escape from local optima, resorting to previous search history. Comparison results show that the algorithm is comparable with the best known EAs, including the winner of the 2005 IEEE Congress on Evolutionary Computation (CEC2005), and significantly better than the others in terms of both the solution quality and computational cost.

Knowledge on the causes, prevention, screening, diagnosis, treatment and progression of disease is increasing exponentially in both volume and complexity. Clinicians and patients need to assimilate this information to make decisions in situations of prognostic uncertainty and healthcare decision aids may help this process by providing all the information (even if conflicting) in one place and/or by aiding values clarification. Like all healthcare interventions, decision aids must be evaluated before introduction into the patient pathway to ensure they provide benefit, avoid harm, and achieve their aims. Published evaluations vary in outcome measures resulting in difficulty in comparisons and limiting progress in this field. This paper reviews the literature and proposes a framework to guide the evaluation of decision aids in healthcare.

It has been suggested that, when faced with large amounts of uncertainty in situations of automated control, type-2 fuzzy logic based controllers will out-perform the simpler type-1 varieties due to the latter lacking the flexibility to adapt accordingly. This paper aims to investigate this problem in detail in order to analyse when a type-2 controller will improve upon type-1 performance. A robotic sailing boat is subjected to several experiments in which the uncertainty and difficulty of the sailing problem is increased in order to observe the effects on measured performance. Improved performance is observed but not in every case. The size of the FOU is shown to be have a large effect on performance with potentially severe performance penalties for incorrectly sized footprints.

Survival analysis describes the analysis of data that corresponds to the time from when an individual enters a study until the occurrence of some particular event or end-point. It is most commonly used in the context of modelling survival (or disease-free interval time) in medical contexts, often concerned with the comparison of survival for different combinations of risk factors and/or treatments. Analytical methods which are transparent to the clinicians in understanding and explaining individual inference need to be considered when dealing with such medical data. In this paper, we present a framework for modelling survival utilising the application of the ANFIS fuzzy inference system. In this framework, alternative methods of partitioning the input space can be selected to define the membership functions, for example by using expert knowledge, equalizer partitioning, fuzzy c-means clustering, or the combination of these techniques. Further, the rule base can be established by enumerating all possible combinations of membership functions of all inputs. After the initialisation of the fuzzy inference structure, the replication data (until time to event) will be subject to be trained using the gradient descent and nonnegative least square algorithm to estimate the conditional event probability. This framework is validated over a novel dataset of patients following operative surgery for ovarian cancer. We demonstrate that the proposed framework can be successfully applied to estimate the hazard and survival curves between different prognostic factors, and model survival times, while providing models with explicit explanation capabilities.

In this paper we describe a method of using interval valued survey responses from multiple experts on multiple occassions to produce General Type-2 fuzzy sets. In the method we propose, both the intra- and inter-person variability are modelled, with no loss of information. The resulting sets are completely determined by the data, providing an accurate representation (in terms of being defined solely by the data) of the opinions being modelled. A description of the method is provided, along with synthetic and real-world numeric examples and a comparison to an alternative method proposed in [1].

An interpretation of the state of health of the baby can be inferred through assessment of the umbilical cord acid-base (UAB) status. This assessment can be made based on pH and other parameters from both arterial and venous blood from the newborn umbilical cord. This can distinguish the cause of a low pH between the distinct physiological conditions of respiratory acidosis due to a short-term accumulation of CO2and a metabolic acidosis (low pH in the tissues) due to lactic acid from a longer-term oxygen deficiency. This UAB assessment suffers the problem of high uncertainty levels between the various experts. Hence, researchers have tried to develop computer based models for the assessment of UAB. Previous research has shown the power of fuzzy logic systems to provide frameworks to handle the encountered uncertainties in real decision making models. Fuzzy Multi-criteria Group Decision Making (MCGDM) has been shown to be an efficient technique for obtaining rankings from experts' opinions. This paper presents a fuzzy logic based multi-criteria group decision making system for the assessment of umbilical cord acid-base. The proposed system models the variation in the decision making process exhibited by the various experts. We will present results which show how the proposed system can give a better agreement with the experts compared to an existing fuzzy expert system (FES).

Fuzzy rule-based systems (FRBS) use the principle of fuzzy sets and fuzzy logic to describe vague and imprecise statements and provide a facility to express the behaviours of the system with a human-understandable language. Fuzzy information, once defined by a fuzzy system, is fixed regardless of the circumstances and therefore makes it very difficult to capture the effect of context on the meaning of the fuzzy terms. While efforts have been made to integrate contextual information into the representation of fuzzy sets, it remains the case that often the context model is very restrictive and/or problem specific. In this work, we introduce a flexible and semantically expressive context representation that can be used in various application scenarios.We also present a practical framework for constructing membership functions of fuzzy sets according to the context within which they are used. An application example concerning the benefits of the new approach in handling context dependency problem over the conventional fuzzy approach are considered.

Both parametric Bayesian mixture and non-parametric Dirichlet process mixture modelling (DPM) approaches for density estimation and clustering allow for automatic model selection. It is interesting to study which approach can better fit the data. In

This paper gives a comprehensive review of the application of meta-heuristics to optimization problems in systems biology, mainly focussing on the parameter estimation problem (also called the inverse problem or model calibration). It is intended for either the system biologist who wishes to learn more about the various optimization techniques available and/or the meta-heuristic optimizer who is interested in applying such techniques to problems in systems biology. First, the parameter estimation problems emerging from different areas of systems biology are described from the point of view of machine learning. Brief descriptions of various meta-heuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying meta-heuristics to the systems biology modelling problem are addressed, including the reliability and identifiability of model parameters, optimal design of experiments, and so on. Finally, we highlight some possible future research directions in this field.

Experimental scientific data sets, especially biology data, usually contain replicated measurements. The replicated measurements for the same object are correlated, and this correlation must be carefully dealt with in scientific analysis. In this paper, we propose a robust Bayesian mixture model for clustering data sets with replicated measurements. The model aims not only to accurately cluster the data points taking the replicated measurements into consideration, but also to find the outliers (i.e., scattered objects) which are possibly required to be studied further. A tree-structured variational Bayes (VB) algorithm is developed to carry out model fitting. Experimental studies showed that our model compares favorably with the infinite Gaussian mixture model, while maintaining computational simplicity. We demonstrate the benefits of including the replicated measurements in the model, in terms of improved outlier detection rates in varying measurement uncertainty conditions. Finally, we apply the approach to clustering biological transcriptomics mRNA expression data sets with replicated measurements.

Type-1 fuzzy logic has frequently been used in control systems. However this method is sometimes shown to be too restrictive and unable to adapt in the presence of uncertainty. In this paper we compare type-1 fuzzy control with several other fuzzy approaches under a range of uncertain conditions. Interval type-2 and non-stationary fuzzy controllers are compared, along with 'dual surface' type-2 control, named due to utilising both the lower and upper values produced from standard interval type-2 systems. We tune a type-1 controller, then derive the membership functions and footprints of uncertainty from the type-1 system and evaluate them using a simulated autonomous sailing problem with varying amounts of environmental uncertainty. We show that while these more sophisticated controllers can produce better performance than the type-1 controller, this is not guaranteed and that selection of Footprint of Uncertainty (FOU) size has a large effect on this relative performance.

There are many issues to be considered in the design of distance-based fuzzy semi-supervised clustering (FSSC) algorithms. To identify these issues, we compare the performance of four such algorithms. We describe the properties of these algorithms, highlighting their key differences, and then experimentally compare their performance on common datasets. Several experimental conditions are investigated. Firstly, two forms of initialisation of the membership values of unlabelled patterns are used; 1/c and 0. Secondly, the algorithms are run with varying proportions of labelled patterns in the datasets, ranging from 2% to 40%. We find that no algorithm outperforms the others in all the datasets. We also observe that small modifications in similar objective functions can improve clustering, and that most of the algorithms perform slightly better with zero initialisation of unlabelled patterns. An interesting observation is that the increase in labelled patterns does not always improve clustering. From these results, we conclude that the number and scale of dimensions in the data set, initial partition matrix, distance metrics and objective functions, together, affect clustering results. In addition, we conclude that not all initially labelled patterns are good candidates for supervision.

In this paper, we describe the main functionality of an initial version of a new fuzzy logic software toolkit based on the R language. The toolkit supports the implementation of several types of fuzzy logic inference systems and we discuss and present several aspects of its capabilities to allow the straightforward implementation of type-1 and interval type-2 fuzzy systems. We include source code examples and visualizations both of type-1 and type-2 fuzzy sets as well as output surface visualizations generated using the R toolkit. Finally, we describe the significant benefits of relying on the R language as a language which is employed across several research disciplines (thus enabling access to fuzzy logic tools to a variety of researchers), outline future developments and most importantly call for contributions, comments and feedback to/on this open-source software development effort.

Type-1 Ordered Weighted Averaging (OWA) operator provides us with a new technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, in which uncertain objects are modeled by fuzzy sets. The Direct Approach to performing type-1 OWA operation involves high computational overhead. In this paper, we define a type-1 OWA operator based on the \alpha-cuts of fuzzy sets. Then, we prove a Representation Theorem of type-1 OWA operators, by which type-1 OWA operators can be decomposed into a series of \alpha-level type-1 OWA operators. Furthermore, we suggest a fast approach, called Alpha-Level Approach, to implementing the type-1 OWA operator. A practical application of type-1 OWA operators to breast cancer treatments is addressed. Experimental results and theoretical analyses show that: 1) the Alpha-Level Approach with linear order complexity can achieve much higher computing efficiency in performing type-1 OWA operation than the existing Direct Approach, 2) the type-1 OWA operators exhibit different aggregation behaviors from the existing fuzzy weighted averaging (FWA) operators, and 3) the type-1 OWA operators demonstrate the ability to efficiently aggregate uncertain information with uncertain weights in solving real-world soft decision-making problems.

In this paper we present an original framework to extract representative groups from a dataset, and we validate it over a novel case study. The framework specifies the application of different clustering algorithms, then several statistical and visualisation techniques are used to characterise the results, and core classes are defined by consensus clustering. Classes may be verified using supervised classification algorithms to obtain a set of rules which may be useful for new data points in the future. This framework is validated over a novel set of histone markers for breast cancer patients. From a technical perspective, the resultant classes are well separated and characterised by low, medium and high levels of biological markers. Clinically, the groups appear to distinguish patients with poor overall survival from those with low grading score and better survival. Overall, this framework offers a promising methodology for elucidating core consensus groups from data.

In this paper, we present a memetic algorithm with novel local optimizer hybridization strategy for constrained optimization. The developed MA consists of multiple cycles. In each cycle, an estimation of distribution algorithm (EDA) with an adaptive univariate probability model is applied to search for promising search regions. A classical local optimizer, called DONLP2, is applied to improve the best solution found by the EDA to a high quality solution. New cycles are employed when the computational budget has not been reached. The new cycles are expected to learn from the search history to make the further search efficient and to enable escape from local optima. The developed algorithm is experimentally compared with ε-DE, which was the winner of the 2006 IEEE Congress on Evolutionary Computation (CEC'06) competition on constrained optimization. The results favour our algorithm against the best-known algorithm in terms of the number of fitness evaluations used to reach the global optimum.

Extracting usable and useful knowledge from large and complex data sets is a difficult and challenging problem. In this paper, we show how two complementary tech-niques have been used to tackle this problem in the con-text of breast cancer. Diagnosis concerns the identifica-tion of cancer within a patient; in contrast, prognosis con-cerns the prediction of the ongoing course of the disease, including issues such as the choice of potential treat-ments such as chemotherapy or drug therapy, in combi-nation with estimation of chances (or length) of survival. Reliable prognosis depends on many factors, including the identification of the type of this heterogeneous dis-ease. We first use a consensus clustering methodol-ogy to identify core, well-characterised sub-groups (or classes) of the disease based on a large database of pro-tein biomarkers from over a thousand patients. We then use fuzzy rule induction and simplification algorithms to generate a simple, comprehensible set of rules for use in future model-based classification. The methods are de-scribed and their use is illustrated on real-world data.

Type-2 fuzzy logic controllers have been used recently for a variety of control problems. In this paper, a novel mechanism is proposed for utilising the lower and upper control surfaces of a conventional interval type-2 fuzzy controller. The new control methodology, termed a `dual-surface' (interval type-2) controller is described and its implementation on micro robots in the context of robot football is presented. Experimental results, both in simulation and in the real world, are presented. It was found that, while the dual-surface controller demonstrated advantages in the simulation experiments, these advantages were not realised in the real-world experiments. We conclude that further and more detailed real-world experiments, in which the real-world uncertainties are carefully considered, are required in order to fully explore whether this novel approach is clearly justified.

Medical prognosis is the prediction of the future course and outcome of a disease and an indication of the likelihood of recovery from that disease. Soft-computing approaches including artificial neural networks and fuzzy inference have been used widely to model expert behaviour. In this paper, we propose the use of an adaptive fuzzy inference system (ANFIS) technique in the estimation of survival prediction. This paper describes the methodology by which ANFIS was used to model survival and presents a comparison of this new method with existing methods in the capability to predict the survival rate in a given medical data set concerning survival of patients following operative surgery for breast cancer.

A mixture of Student t-distributions (MoT) has been widely used to model multivariate data sets with atypical observations, or outliers for robust clustering. In this paper, we developed a novel robust clustering approach by modeling the data sets using mixture of Pearson type VII distributions (MoP). An EM algorithm is developed for the maximum likelihood estimation of the model parameters. An outlier detection criterion is derived from the EM solution. Controlled experimental results on the synthetic datasets show that the MoP is more viable than the MoT. The MoP performs comparably if not better, on average, in terms of outlier detection accuracy and out-of-sample log-likelihood with the MoT. Furthermore, we compared the performances of the Pearson type VII and the student t mixtures on the classification of several benchmark pattern recognition data sets. The comparison favours the developed Pearson type VII mixtures.

Yager's ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts' individual opinions or preferences for achieving an overall decision. The traditional Yager's OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. Type-2 fuzzy sets provide an efficient way of knowledge representation for modeling linguistic terms. In order to aggregate linguistic opinions via OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator, to aggregate the linguistic opinions or preferences in human decision making modeled by type-2 fuzzy sets. A Direct Approach to aggregating interval type-2 fuzzy sets by type-2 OWA operator is suggested in this paper. Some examples are provided to delineate the proposed technique. © 2010 Wiley Periodicals, Inc.

Automatic protein structure predictors use the notion of energy to guide the search towards good candidate structures. The energy functions used by the state-of-the-art predictors are defined as a linear combination of several energy terms designed by human experts. We hypothesised that the energy based guidance could be more accurate if the terms were combined more freely. To test this hypothesis, we designed a genetic programming algorithm to evolve the protein energy function. Using several different fitness functions we examined the potential of the evolutionary approach on a set of candidate structures generated during the protein structure prediction process. Although our algorithms were able to improve over the random walk, the fitness of the best individuals was far from the optimum. We discuss the shortcomings of our initial algorithm design and the possible directions for further research.

Data mining is the analysis of experimental datasets to extract trends and relationships that can be meaningful for the user. In genetic studies these techniques have revealed interesting findings, especially in the heritable predisposition to contract specific diseases. One of these diseases which is still under extensive analysis is pre-eclampsia, a progressive disorder which occurs during pregnancy and soon after the birth, affecting both the mothers and their babies. There are many choices to be made in the application of the various data mining techniques that may be used to study general genotype-phenotype associations. The aim of this paper is to describe the general framework that we adopted in the application of decision tree algorithms to the analysis of SNPs data related to cases of pre-eclampsia. The results show the validity of this methodology to detect a subset of attributes associated with the predictable variable, providing a reduction in the size of the dataset. Moreover, from the clinical point of view, it confirmed the medical interpretation of the ‘corrected birth-weight centile’ (CBC) value of 10 being a meaningful cut-off and confirmed association between an infant's CBC and the ‘week of delivery’ parameter. We hope that the generic framework described here will be of use to other researchers analysing such data.

In this paper we compare the differences between type-1 and interval type-2 fuzzy logic controllers, with seven, five and two three term membership functions. The controllers were used to control a DC motor model in a closed loop simulation. The performance of each controller to a step change and a change in motor inertia with and without added noise was recorded. The results showed that there was no statistical difference between the type-1 and type-2 controllers. It was also found that a type-1 three term controller was as good as a type-1 or type-2 seven term controller, in controlling the micro robot DC motor model.

The use of linguistic rulesets is considered one of the greatest advantages that fuzzy classification systems can offer compared to non-fuzzy classification systems. This paper proposes the use of fuzzy thresholds and fuzzy quantifiers for generating linguistic rulesets from a data-driven fuzzy subsethood-based classification system. The proposed technique offers not only simplicity in the design and comprehensibility of the generated rulesets but also practicality in the implementation. Additionally, the use of fuzzy quantifiers makes it easier for the user to understand the classification process and how such classifications were reached. The effectiveness of the proposed method is demonstrated using a medical dataset which provides evidence that rules generated by the proposed system are consistent with the expert-rules created by clinicians.

Recommending appropriate follow-up treatment options to patients after diagnosis and primary (usually surgical) treatment of breast cancer is a complex decision making problem. Often, the decision is reached by consensus from a multi-disciplinary team of oncologists, radiologists, surgeons and pathologists. Non-stationary fuzzy sets have been proposed as a mechanism to represent and reason with the knowledge of such multiple experts. In this paper, we briefly describe the creation of a non-stationary fuzzy inference system to provide decision support in this context, and examine a number of alternative methods for interpreting the output of such a non-stationary inference system. The alternative interpretation methodologies and the experiments carried out to compare these methods are detailed. Results are presented which shown that using majority voting ensemble decision making from a non-stationary fuzzy system improves accuracy of the decision making. We conclude that non-stationary systems coupled with ensemble interpretation methods are worthy of further exploration.

In this paper, a novel type-1 OWA based non-stationary fuzzy system is proposed, in which the type-1 OWA operator is used in the fuzzy inference process to aggregate the non-stationary fuzzy outputs. The advantage of non-stationary fuzzy sets lies in their ability to model expert's variations in automated decision support systems. The proposed scheme offers an opportunity to combine different uncertain objects with uncertain weights into an overall decision in the fuzzy inference process. The agreement achieved between the proposed fuzzy system and clinical expert decision in selecting optimal treatment plans is used to evaluate the performance of the method. The experimental results on post-operative breast cancer treatments have demonstrated that the proposed fuzzy system can effectively diagnose breast cancer treatment in decision supports.

This work examines the dendritic cell algorithm (DCA) from a mathematical perspective. By representing the signal processing phase of the algorithm using the dot product it is shown that the signal processing element of the DCA is actually a collection of linear classifiers. It is further shown that the decision boundaries of these classifiers have the potentially serious drawback of being parallel, severely limiting the applications for which the existing algorithm can be potentially used on. These ideas are further explored using artificially generated data and a novel visualisation technique that allows an entire population of dendritic cells to be inspected as a single classifier. The paper concludes that the applicability of the DCA to more complex problems is highly limited.

The implementation of a robotic security solution generally requires one algorithm to route the robot around the environment and another algorithm to perform anomaly detection. Solutions to the routing problem require the robot to have a good estimate of its own pose. We present a novel security system that uses metrics generated by the localisation algorithm to perform adaptive anomaly detection. The localisation algorithm is a vision-based SLAM solution called RatSLAM, based on mechanisms within the hippocampus. The anomaly detection algorithm is based on the mechanisms used by the immune system to identify threats to the body. The system is explored using data gathered within an unmodified office environment. It is shown that the algorithm successfully reacts to the presence of people and objects in areas where they are not usually present and is tolerised against the presence of people in environments that are usually dynamic.

BACKGROUND: Statistical analysis of DNA microarray data provides a valuable diagnostic tool for the investigation of genetic components of diseases. To take advantage of the multitude of available data sets and analysis methods, it is desirable to combine both different algorithms and data from different studies. Applying ensemble learning, consensus clustering and cross-study normalization methods for this purpose in an almost fully automated process and linking different analysis modules together under a single interface would simplify many microarray analysis tasks. RESULTS: We present ArrayMining.net, a web-application for microarray analysis that provides easy access to a wide choice of feature selection, clustering, prediction, gene set analysis and cross-study normalization methods. In contrast to other microarray-related web-tools, multiple algorithms and data sets for an analysis task can be combined using ensemble feature selection, ensemble prediction, consensus clustering and cross-platform data integration. By interlinking different analysis tools in a modular fashion, new exploratory routes become available, e.g. ensemble sample classification using features obtained from a gene set analysis and data from multiple studies. The analysis is further simplified by automatic parameter selection mechanisms and linkage to web tools and databases for functional annotation and literature mining. CONCLUSION: ArrayMining.net is a free web-application for microarray analysis combining a broad choice of algorithms based on ensemble and consensus methods, using automatic parameter selection and integration with annotation databases.

In our previous work Li et al., in Proc of 3rd IEEE Int Workshop on Engineering of Automatic & Automation Systems, Potsdam, Germany, 2006, pp 25–34; Li et al., in Proc Workshop on Nature Inspired Cooperative Strategies for Optimization, Granada, Spain, 2006, pp 123–134, we introduced automated self-assembly programming paradigm (ASAP2) using unguided self-assembly and swarm-inspired methodologies. We investigated how external environment settings affect software self-assembly speed and diversity of the generated programs. In this paper, we extend our previous work with a diversified compartments approach based on general graphs. This diversified compartments approach is integrated into a network structure such that each compartment can be seen as a node in the network. We investigate how structures of the network impacts on software self-assembly speed, complexity, and diversity of generated programs. Results indicate that network structure can substantially affect the dynamics, diversity, and complexity of generated programs. © 2009 Wiley Periodicals, Inc.

Type-2 fuzzy systems are increasing in popularity, and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type-1 fuzzy systems, there is a lack of such techniques for type-2 systems. The essential problem is to reduce the number of rules, while maintaining the system's approximation performance. In this paper, four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, which are termedR-values,c-values, omega1-values, and omega2-values. TheR-values of type-2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. Thec-values rank rules based on the effects of rule consequents, while the omega1-values and omega2-values consider both the rule-base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilizing these indexes in fuzzy rule selection (termed ldquoforward selectionrdquo and ldquobackward eliminationrdquo) are described. Experiments are presented which demonstrate that by using the proposed methodology, the most influential type-2 fuzzy rules can be effectively retained in order to construct parsimonious type-2 fuzzy models.

Developing a treatment plan for breast cancer patient is a very complex process. In this paper, we propose a scheme of inducing fuzzy rules that characterise breast caner treatment knowledge from data. These fuzzy rules can augment the human experts in the process of medical diagnosis to select optimal treatment for patients. The proposed machine learning scheme applies the particle swarm optimisation technique (PSO) to the construction of an optimal support vector machine (SVM) model for the sake of inducing accurate and parsimonious fuzzy rules and simultaneously reducing input space dimensions, in which a new fittness function that regularises the importance ranks of features with misclassification rate is suggested. The SVM-based fuzzy classifier evades the curse of dimensionality in high-dimensional breast cancer data space in the sense that the number of support vectors, which equals the number of induced fuzzy rules, is not related to the dimensionality. The experiments have shown that not only the classification performance achieved by the proposed fuzzy classifier outperforms the ones achieved by other methods in the literature, but also the input space dimension has been reduced greatly.

In this paper we propose the concept of an instantiative fuzzy set which, in our opinion, constitutes a meaningful addition to the notion of a non-stationary fuzzy set. We begin with a formal definition of an instantiative fuzzy set, and follow specifying basic classes of instantiative fuzzy set operators: the union, the intersection and the complement. Furthermore, we provide formal definitions of selected notions relevant to instantiative fuzzy sets. At the end, we present a subclasses of instantiative fuzzy sets that might be useful for dealing with randomness and vagueness simultaneously. The work presented in this paper is at a very preliminary stage; it is meant as a starting point to a formal discussion on the capture of different facets of uncertainty.

This paper describes and further extends the fuzzy inferencing system which won the simulated car racing competition that was arranged as part of FuzzlEEE 2007 conference. The details of the winning non-stationary fuzzy controller and its results are presented. A novel approach to further improve the performance of the winning controller is described and formalised. We term the new fuzzy inferencing method a dasiacontext-dependentfuzzyinferencesystempsila. The concept of a dasiacontext-dependentfuzzysetpsila that is utilised by the fuzzy system is introduced. Finally, a comparison between context-dependent fuzzy inference system and various existing techniques are carried out on the simulated car racing application. The results show a better performance for context-dependent fuzzy inference systems in stochastic circumstances.

Yager’s ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts’ individual opinions or preferences for achieving an overall decision. The traditional Yager’s OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms, like “important” , “very important”, “good” etc.. Type-2 fuzzy sets provide an efficient way of knowledge representation for modelling linguistic terms. In order to aggregate linguistic opinions via the OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator that is able to aggregate type-2 fuzzy sets, and therefore to aggregate the linguistic opinions or preferences in human decision making. The necessary equations for performing type-2 OWA operations on aggregating interval type-2 fuzzy sets are derived in this paper. Some examples are provided to illustrate the proposed technique.

The classification of breast cancer patients is of great importance in cancer diagnosis. During the last few years, many algorithms have been proposed for this task. In this paper, we review different supervised machine learning techniques for classification of a novel dataset and perform a methodological comparison of these. We used the C4.5 tree classifier, a multilayer perceptron and a naive Bayes classifier over a large set of tumour markers. We found good performance of the multilayer perceptron even when we reduced the number of features to be classified. We found naive Bayes achieved a competitive performance even though the assumption of normality of the data is strongly violated.

In this paper, the notion termed a ldquononstationary fuzzy setrdquo is introduced, and the concept of a perturbation function that is used for generating nonstationary fuzzy sets is presented. Definitions of the basic set operators (the union, the intersection, and the complement) for nonstationary fuzzy sets are given, together with proofs of selected properties of these operators. Two case studies were carried out in order to illustrate the use of nonstationary fuzzy sets in a nonstationary fuzzy inference, and to provide an initial insight into the relationships between nonstationary and interval type-2 fuzzy sets.

This paper considers the problem of grid scheduling in which different jobs are assigned to different processors, and a scheduling algorithm is devised, using tabu search, to find optimal solutions in order to maximize the number of scheduled jobs. However, inherent in the nature of the application, the processing times of jobs are not precise but are estimates that vary between minimal values, in case of premature failure of jobs, to maximal values as specified 'a priori' by well-experienced users. Fuzzy methodology becomes instrumental in this application as it allows the use of fuzzy sets to represent the processing times of jobs, modelling their uncertainty. This work presents the implementation of a tabu search algorithm to create good schedules and explores the robustness of the schedule when processing times do vary by assessing its performance in both fuzzy and crisp modes. Finally, the impact of changing the shapes of fuzzy completion times and the average job length on the schedule performance is discussed.

In this paper, formal definitions of the concepts relevant to non-stationary fuzzy sets are provided, as well as definitions of the basic non-stationary fuzzy set operators with proofs of selected properties of these operators. Among the novel terms introduced are the footprint of instantiations, the domain of instantiations and the temporal histogram. Further, we discuss the correspondence between non-stationary and type-2 fuzzy sets, and make the first attempt at proposing a set of comparable terms.

In this paper, we propose two novel indices for type-2 fuzzy rule ranking to identify the most influential fuzzy rules in designing type-2 fuzzy logic systems, and name them as R-values and c-values of fuzzy rules separately. The R-values of type-2 fuzzy rules are obtained by applying QR decomposition in which there is no need to estimate a rank as required in the SVD-QR with column pivoting algorithm. The c-values of type-2 fuzzy rules are suggested to rank rules based on the effects of rule consequents. Experimental results on a signal recovery problem have shown that by using the proposed indices the most influential type-2 fuzzy rules can be effectively selected to construct parsimonious type-2 fuzzy models while the system performances are kept at a satisfied level.

This paper presents a case study in which the introduction of vagueness or uncertainty into the membership functions of a fuzzy system was investigated in order to model the variation exhibited by experts in a medical decision-making context. A conventional (type-1) fuzzy expert system had previously been developed to assess the health of infants immediately after birth by analysis of the biochemical status of blood taken from infants' umbilical cords. Variation in decision making was introduced into the fuzzy expert system by means of membership functions which altered in small, predetermined manners over time. Three types of variation in membership functions were investigated: i) variation in the centre points, ii) variation in the widths, and iii) the addition of "white noise". Different levels (amounts) of uniformly distributed random variation were investigated for each of these types. Monte Carlo simulations were carried out to propagate the variation through the inferencing process in order to determine distributions of the conclusions reached. Interval valued type-2 fuzzy systems were also implemented to investigate the boundaries of variability in decisions. The results obtained were compared to the experts' decisions in order to determine which type and size of membership function variability best matched the experts' variability. The novel reasoning technique introduced in this study is termed nonstationary fuzzy reasoning

Jerne's idiotypic-network theory postulates that the immune response involves interantibody stimulation and suppression, as well as matching to antigens. The theory has proved the most popular artificial immune system (AIS) model for incorporation into behavior-based robotics, but guidelines for implementing idiotypic selection are scarce. Furthermore, the direct effects of employing the technique have not been demonstrated in the form of a comparison with nonidiotypic systems. This paper aims to address these issues. A method for integrating an idiotypic AIS network with a reinforcement-learning (RL)-based control system is described, and the mechanisms underlying antibody stimulation and suppression are explained in detail. Some hypotheses that account for the network advantage are put forward and tested using three systems with increasing idiotypic complexity. The basic RL, a simplified hybrid AIS-RL that implements idiotypic selection independently of derived concentration levels, and a full hybrid AIS-RL scheme are examined. The test bed takes the form of a simulated Pioneer robot that is required to navigate through maze worlds detecting and tracking door markers.

The aim of this study was to explore relationships between the shape of the primary membership functions and the uncertainties obtained in the output sets for both non-stationary and interval type-2 fuzzy systems. The study was carried out on a fuzzy system implementing the standard XOR problem, in which either Gaussian or triangular membership functions were employed, using a range of input values and recording the size of the output intervals obtained. It can be observed that the shape of the surfaces of the output intervals are related to the primary membership function and that the surface is divided into four roughly symmetrical parts. Furthermore, it can be observed that there are complex differences between the surfaces produced by interval type-2 systems and various kinds of non-stationary systems. Detailed differences between the output surfaces of uniformly distributed non-stationary systems are examined and the implications are discussed.

In this paper a notion termed nonstationary fuzzy sets is introduced and the concept of random perturbations that can be used for generating these nonstationary fuzzy sets is also presented. A case study was carried out to investigate the relationship between the performance of nonstationary fuzzy logic systems and interval type-2 fuzzy logic systems. It can be observed that in case of centre variation, the lower-upper boundaries of outputs predicted by nonstationary systems are slightly narrower than those from the corresponding interval type-2 systems. On the other hand, in case of width variation, the lower-upper boundaries of outputs predicted by nonstationary systems are slightly wider than those from the type-2 systems. Moreover, an interesting observation is that the secondary membership function of the type-2 sets corresponding to nonstationary fuzzy sets generated using normally distributed perturbations are nonuniform. In contrast to noninterval type-2 sets, this does not affect the inference process of the nonstationary sets. In this sense, the use of nonstationary fuzzy sets may enable approximations to be made of general type-2 fuzzy inferencing

Terms used in fuzzy systems are almost invariably normalised, convex and distinct. The shapes of these terms are generated by certain accepted membership functions: piecewise linear functions, Gaussians or Sigmoids are almost exclusively used. This paper extends previous work in which it was suggested that non-convex membership functions might be considered for use in the context of modelling human decision making utilising fuzzy expert systems. In particular, the merits of non-convex fuzzy sets are discussed and a case study is presented to investigate inferencing with non-convex fuzzy sets in a practical implementation. It is shown that it is indeed possible to build a fuzzy expert system featuring usual Mamdani style fuzzy inference in which a time-related non-convex fuzzy set is used together with 'traditional' fuzzy sets. An examination is made of the resultant output surface generated by four different sub-classes of non-convex membership functions.

This paper explains how the shape of type-2 fuzzy membership functions can be used to model the variation in human decision making. An interval type-2 fuzzy logic system (FLS) is developed for umbilical acid-base assessment. The influence of the shape of the membership functions on the variation in decision making of the fuzzy logic system is studied using the interval outputs. Three different methods are used to create interval type-2 membership functions. The centre points of the primary membership functions are shifted, the widths are shifted, and a uniform band is introduced around the original type-1 membership functions. It is shown that there is a direct relationship between the variation in decision making and the uncertainty introduced to the membership functions.

The shapes of terms used in fuzzy systems have adopted several 'conventions'. Terms are almost invariably normalised (having a maximum membership value of 1), convex (having a single maximum or plateau maxima) and distinct (being restricted in their degree of overlap: often expressed as some variation on the concept that all membership values at any point in the universe of discourse sum to I across that universe). The shape of these terms are generated by certain accepted membership functions: piecewise linear functions (with restrictions), Gaussians or Sigmoids are almost exclusively used. As such these constitute only a small subset of the total set of possible shapes of terms. These conventions are largely empirical or are justified by arguments based on what might loosely be called 'fuzzy control principles'. The paper highlights a number of membership functions that developers of fuzzy systems outside the paradigm of fuzzy control may consider as alternatives. In particular, we highlight subsumed fuzzy sets, discuss the merits of non-convex fuzzy sets and present a medical application where sub-normal fuzzy sets have been used. These ideas are reinforced by examples.

Camera motion estimation is useful for a range of applications. Usually, feature tracking is performed through the sequence of images to determine correspondences. Furthermore, robust statistical techniques are normally used to handle large number of outliers in correspondences. This paper proposes a new method that avoids both. Motion is calculated between two consecutive stereo images without any pre-knowledge or prediction about feature location or the possibly large camera movement. This permits a lower frame rate and almost arbitrary movements. Euclidean constraints are used to incrementally select inliers from a set of initial correspondences, instead of using robust statistics that has to handle all inliers and outliers together. These constraints are so strong that the set of initial correspondences can contain several times more outliers than inliers. Experiments on a worst-case stereo sequence show that the method is robust, accurate and can be used in real-time.

Fuzzy logic and fuzzy set theory provide an important framework for representing and managing imprecision and uncertainty in medical expert systems, but the need remains to optimize such systems to enhance performance. The paper presents a general technique for optimizing fuzzy models in fuzzy expert systems (FESs) by simulated annealing (SA) and N-dimensional hill climbing simplex method. The application of the technique to a FES for the interpretation of the acid-base balance of blood in the umbilical cord of newborn infants is presented. The Spearman rank order correlation statistic was used to assess and to compare the performance of a commercially available crisp expert system, an initial FES, and a tuned FES with experienced clinicians. Results showed that without tuning, the performance of the crisp system was significantly better (correlation of 0.80) than the FES (correlation of 0.67). The performance of the tuned FES was better than the crisp system and effectively indistinguishable from the clinicians (correlation of 0.93) on training data and was the best of the expert systems on validation data. Unlike most applications of fuzzy logic where all fuzzy sets have normalized heights of unity, in this application it was found that a reduction in the height of some fuzzy sets was effective in enhancing performance. This suggests that the height of fuzzy sets may be a generally useful parameter in tuning FESs.