Federated Fuzzy C-Means (FCM) clustering methods have demonstrated success in standard federated learning (FL) environments, but model heterogeneity presents a significant challenge. This heterogeneity hampers communication content selection and makes traditional aggregation methods, such as federated averaging (FedAvg), insufficient for diverse client models. Additionally, handling non-IID data distributions and learning robust feature representations remain unresolved in some existing approaches. To tackle these issues, we propose FFCMD, a federated FCM clustering framework designed to address model heterogeneity while enhancing feature learning and accommodating non-IID data. FFCMD integrates an autoencoder (AE) with a fuzzy C-Means network (FCMN), augmented by mutual knowledge distillation (mKD), to improve data feature learning, communication, and aggregation under heterogeneous conditions. The AE incorporates a clustering-oriented penalty term to learn discriminative features, boosting performance on complex datasets. Rather than direct parameter aggregation, mKD updates the global model using local devices' soft assignments, naturally handling structural variations across client models. Moreover, FFCMD employs discrepancy-aware weighting mechanisms to dynamically align local and global category distributions during soft assignment embedding, effectively addressing the challenges posed by non-IID data. Extensive experiments on multiple public datasets show that FFCMD outperforms state-of-the-art methods, particularly in non-IID scenarios, and excels even in the presence of model heterogeneity.

Sliding cardinality estimation is crucial in many data analysis scenarios, e.g., detecting abnormal network behav-iors by monitoring unique connections in real time, detecting fraud in online transactions by monitoring unique user behavior patterns, and improving inventory management in supply chains by analyzing unique buyer behaviors. However, existing sliding cardinality estimation methods suffer from a cardinality barrel-down problem caused by unexpired item elimination in advance and item excessive removal, which remains unresolved so far. In this paper, we propose TardySketch, a sketch framework to make sliding cardinality estimation accurate and efficient by solving the above problem. The cornerstone of TardySketch is a Bidirectional Pointer-based Bitmap (BP-Bitmap), which stores the arrival sequence of items without timestamps. To prevent the premature elimination of unexpired items, we propose a Gap mechanism to enhance the accuracy of BP-Bitmap for identifying truly expired items through intermittent monitoring. To ensure an appropriate number of items are eliminated as the window moves, we design a Slow-Down mechanism to slacken the reset rate of bucket in BP- Bitmap to prevent over removal of items. Experimental results based on real-world datasets demonstrate that TardySketch significantly outperforms state-of-the-art methods, achieving a performance improvement of 5–40 times. The source code of TardySketch is available on GitHub.

Heterogeneous graph neural network (HGNN) is a popular technique for modeling and analyzing heterogeneous graphs. Most existing HGNN-based approaches are supervised or semi-supervised learning methods requiring graphs to be annotated, which is costly and time-consuming. Self-supervised contrastive learning has been proposed to address the problem of requiring annotated data by mining intrinsic properties in the given data. However, the existing contrastive learning methods are not suitable for heterogeneous graphs because they construct contrastive views only based on data perturbation or pre-defined structural properties (e.g., meta-path) in graph data while ignoring noises in node attributes and graph topologies. We develop a robust heterogeneous graph contrastive learning approach, namely HGCL, which introduces two views on respective guidances of node attributes and graph topologies and integrates and enhances them by a reciprocally contrastive mechanism to better model heterogeneous graphs. In this new approach, we adopt distinct but suitable attribute and topology fusion mechanisms in the two views, which are conducive to mining relevant information in attributes and topologies separately. We further use both attribute similarity and topological correlation to construct high-quality contrastive samples. Extensive experiments on four large real-world heterogeneous graphs demonstrate the superiority and robustness of HGCL over several state-of-the-art methods.

Multi-label feature selection is an effective approach to mitigate the high-dimensional feature problem in multi-label learning. Most existing multi-label feature selection methods either assume that the data is complete, or that either the features or the labels are incomplete. So far, there are few studies on multi-label data with missing features and labels. In many cases, missing features in instances of multi-label data often lead to missing labels, which is ignored by existing studies. We define this type of data as instance-dependent incomplete multi-label data. In this paper, we propose a feature selection method for instance-dependent incomplete multi-label data. Firstly, we use the positive correlations between features to reconstruct the feature space, thereby recovering missing values and enhancing non-missing values. Secondly, we use fuzzy tolerance relation to guide label recovery, and utilize fuzzy mutual implication granularity to impose structural constraint on the projection matrix. Thirdly, we achieve feature selection by eliminating the impact of incomplete instances and imposing sparse regularization on the projection matrix. Finally, we provide a convergent solution for the proposed feature selection framework. Comparative experiments with existing multi-label feature selection methods show that our method can perform effective feature selection on instance-dependent incomplete multi-label data.

Outlier detection refers to the identification of anomalous samples that deviate significantly from the distribution of normal data and has been extensively studied and used in a variety of practical tasks. However, most unsupervised outlier detection methods are carefully designed to detect specified outliers, while real-world data may be entangled with different types of outliers. In this study, we propose a fuzzy rough sets-based multi-scale outlier detection method to identify various types of outliers. Specifically, a novel fuzzy rough sets-based method that integrates relative fuzzy granule density is first introduced to improve the capability of detecting local outliers. Then, a multi-scale view generation method based on granular-ball computing is proposed to collaboratively identify group outliers at different levels of granularity. Moreover, reliable outliers and inliers determined by the three-way decision are used to train a weighted support vector machine to further improve the performance of outlier detection. The proposed method innovatively transforms unsupervised outlier detection into a semi-supervised classification problem and for the first time explores the fuzzy rough sets-based outlier detection from the perspective of multi-scale granular balls, allowing for high adaptability to different types of outliers. Extensive experiments carried out on both artificial and UCI datasets demonstrate that the proposed outlier detection method significantly outperforms the state-of-the-art methods, improving the results by at least 8.48% in terms of the Area Under the ROC Curve (AUROC) index. The source codes are released at https://github.com/Xiaofeng-Tan/MGBOD

Contrastive Learning (CL) has emerged as a popular self-supervised representation learning paradigm that has been shown in many applications to perform similarly to traditional supervised learning methods. A key component of CL is mining the latent discriminative relationships between positive and negative samples and using them as self-supervised labels. We argue that this discriminative contrastive task is, in essence, similar to a classification task, and the “either positive or negative” hard label sampling strategies are arbitrary. To solve this problem, we explore ideas from data distillation, which considers probabilistic logit vectors as soft labels to transfer model knowledge. We attempt to abandon the classical hard sampling labels in CL and instead explore self-supervised soft labels. We adopt soft sampling labels that are extracted, without supervision, from the inherent relationships in data pairs to retain more information. We propose a new self-supervised graph learning method, Distill and Contrast (D&C), for learning representations that closely approximate natural data relationships. D&C extracts node similarities from the features and structures to derive soft sampling labels, which also eliminate noise in the data to increase robustness. Extensive experimental results on real-world datasets demonstrate the effectiveness of the proposed method.

In multisource information fusion (MSIF), Dempster–Shafer evidence (DSE) theory offers a useful framework for reasoning under uncertainty. However, measuring the divergence between belief functions within this theory remains an unresolved challenge, particularly in managing conflicts in MSIF, which is crucial for enhancing decision-making level. In this paper, several divergence and distance functions are proposed to quantitatively measure discrimination between belief functions in DSE theory, including the reverse evidential KullbackLeibler (REKL) divergence, evidential Jeffrey’s (EJ) divergence, evidential JensenShannon (EJS) divergence, evidential$\chi ^{2}$(E$\chi ^{2}$) divergence, evidential symmetric$\chi ^{2}$(ES$\chi ^{2}$) divergence, evidential triangular (ET) discrimination, evidential Hellinger (EH) distance, and evidential total variation (ETV) distance. On this basis, a generalized$f$-divergence, also called the evidential$f$-divergence (Ef divergence), is proposed. Depending on different kernel functions, the Ef divergence degrades into several specific classes: EKL, REKL, EJ, EJS, E$\chi ^{2}$and ES$\chi ^{2}$divergences, ET discrimination, and EH and ETV distances. Notably, when basic belief assignments (BBAs) are transformed into probability distributions, these classes of Ef divergence revert to their classical counterparts in statistics and information theory. In addition, several Ef-MSIF algorithms are proposed for pattern classification based on the classes of Ef divergence. These Ef-MSIF algorithms are evaluated on real-world datasets to demonstrate their practical effectiveness in solving classification problems. In summary, this work represents the first attempt to extend classical$f$-divergence within the DSE framework, capitalizing on the distinct properties of BBA functions. Experimental results show that the proposed Ef-MSIF algorithms improve classification accuracy, with the best-performing Ef-MSIF algorithm achieving an overall performance difference approximately 1.22 times smaller than the suboptimal method and 14.12 times smaller than the worst-performing method.

In this paper, a multi-object recognition scenario is considered to extend the random finite set into random permutation set. Probabilistic information on random permutation set can be viewed as an distribution determined by three random variables. We use another emerging uncertainty representation, order-2 information granule, to realize the probabilistic information fusion on random permutation sets. First, the probabilistic information on random permutation sets is viewed as an order-2 probability distribution. Second, corresponding information fusion approach is proposed. Finally, the proposed approach is applied to random permutation sets, resolving the decision-making issue under the multi-object recognition scenario. This paper pioneers the connection of order-2 information processing logic to a multi-object recognition task and develops order-2 probability distribution and its combination rules. Compared to the traditional probabilistic information fusion approaches, the proposed approach takes into account not only the propositions’ beliefs provided by the sources, but the structural dependency among propositions as well.

Feature selection plays a significant role in data mining and machine learning. It is challenging to determine how many features are necessary to form an optimal feature subset. To address this challenge, an innovative visual 2D feature selection framework is introduced, in which the feature discernibility and independence are defined to evaluate its capability for classification and its relevance to other features, respectively. All features are represented in 2D space with discernibility as$x$-axis and independence as$y$-axis. The features located in the upper right corner represent high discernibility and high independence, so comprise the optimal feature subset. This leads to the formation of a family of feature selection algorithms. Three such algorithms are proposed in this paper referred to as FSDIE, FSDIR, and FSDIS (Feature Selection based on the Discernibility and the Independence, respectively, of Exponent, Reciprocal, and anti-Similarity). To speed-up these three algorithms, a clustering based feature preselection first eliminates some unrelated and redundant features. Extensive experiments on UCI datasets, face datasets and gene expression datasets demonstrate that these three 2D feature selection algorithms are superior to the state-of-the-art methods indicating the power of our 2D feature selection framework.

Knowledge discovery of heterogeneous data is an active topic in knowledge engineering. Feature selection for heterogeneous data is an important part of effective data analysis. Although there have been many attempts to study the feature selection for heterogeneous data, there are still some challenges, such as the unbalanced problem between the stability and validity of the designed model. Hence, this paper focuses on how to design an effective and robust heterogeneous feature selection method, namely a zentropy-based uncertainty measure for heterogeneous feature selection(Ze-HFS). Different from other entropy-based uncertainty measures, the proposed method does not consider single-level information measures but systematically analyzes and integrates the information between different granular levels, which has an obvious advantage in the study of heterogeneous data knowledge discovery. Specifically, a heterogeneous distance metric is first introduced to construct heterogeneous neighborhood granules and heterogeneous neighborhood rough sets(HNRS). Then, the zentropy-based uncertainty measure is developed by analyzing the granular level structure in the HNRS model. Finally, two significant measures based on the above research are designed for heterogeneous feature selection. Compared with other state-of-the-art methods, the experimental results on 18 public datasets demonstrate the robustness and effectiveness of the proposed method.

This study is devoted to the design of gradient boosted fuzzy rule-based models for regression problems. Fuzzy rule-based models are built on the basis of information granules formed in the input and output spaces whose structure involves a family of conditional ‘if-then’ statements. The architecture of fuzzy rule-based models contributes to the realization of a sound tradeoff between modeling accuracy and interpretability and computing overhead. Gradient boosting paradigm has emerged as a powerful learning method realized through sequentially fitting additive base learners to current residuals in the steepest descent way. However, surprisingly, studies on the design and analysis of gradient boosted fuzzy rule-based models are still lacking. In this study, fuzzy rule-based model is regarded as a base learner. Different loss functions and their influence on the performance of the final models are explored. We also thoroughly investigate an impact of the initial quality of the rule-based model (implied by the number of rules) on the process of gradient boosting. The performance of the proposed approach is illustrated by a series of experimental studies concerning synthetic and publicly available datasets.

Multi-view learning becomes increasingly attractive and promising because multimodal or multi-view data are commonly encountered in real-world applications. In this study, we develop a novel multi-view Takagi–Sugeno–Kang (TSK) fuzzy system framework to handle classification problems for such data. We propose an anchor and graph subspace clustering strategy to discover and represent the actual latent data distribution for each view separately. In this way, the discriminate anchors (landmarks) are learned to capture the main structure of the multi-view data. This strategy also provides a computationally efficient clustering algorithm with respect to the number of instances. These resulting anchors are formed as the prototypes of information granules (IGs) for fuzzy modeling. Then we construct an information-granule-based multi-view TSK fuzzy classification model inherited from the natural interpretability of fuzzy rule-based systems. Concretely, the relationship between the multi-view input and label output spaces is depicted by IGs-oriented fuzzy rules. The experimental studies involve various commonly used benchmark datasets, which indicate that our proposed method achieves comparable or better performance compared to the state-of-the-art algorithms.

Fuzzy C-Means (FCM) is a widely used clustering method. However, FCM and its many accelerated variants have low efficiency in the mid-to-late stage of the clustering process. In this stage, all samples are involved in updating their non-affinity centers, and the membership grades of most samples, whose assignments remain unchanged, are still updated by calculating the sample-center distances. All these factors lead to the algorithms converging slowly. In this paper, a new affinity filtering technique is developed to recognize a complete set of non-affinity centers for each sample with low computations. Then, a new membership scaling technique is suggested to set the membership grades between each sample and its non-affinity centers to 0 and maintain the fuzzy membership grades for others. By integrating these two techniques, FCM based on new affinity filtering and membership scaling (AMFCM) is proposed to accelerate the whole convergence process of FCM. Numerous experimental results performed on synthetic and real-world data sets have shown the feasibility and efficiency of the proposed algorithm. Compared with state-of-the-art algorithms, AMFCM is significantly faster and more effective. For example, AMFCM reduces the number of FCM iterations by 80$\%$on average.

In decision-making systems, how to address uncertainty plays an important role for the improvement of system performance in uncertainty reasoning. Dempster—Shafer evidence (DSE) theory is an effective method to address uncertainty in decision-making problems by means of basic belief assignments (BBAs) and Dempster's combination rule. In the DSE theory, divergence measure between BBAs, which is beneficial for conflict information management in decision making, remains an open issue. In this paper, several generalized evidential divergences (EDs) are proposed and studied to measure the difference and discrepancy between BBAs in DSE theory, which have more universal applicability in decision theory. On this basis, a uniform BJS divergence-based decision-making algorithm is devised to improve the decision level. Furthermore, the extensions of weighted BJS to decision-making algorithms are discussed by considering not only subjective weights but also objective weights. Notably, this is the first work to propose the weighted BJS divergence in DSE theory providing a promising way to analyze decision-making problems from different perspectives. Finally, the proposed BJS-based decision-making algorithm is applied to pattern classification. The results validate that the proposed decision-making algorithm is beneficial for diverse real-world datasets and outperforms several well-known related works and demonstrates higher classification accuracy as well as robustness.

The performance of k-means clustering is often degenerate when dealing with high-dimensional and noisy scenarios. In this study, an end-to-end robust clustering method with low-rank linear embedding techniques (RCLR) is presented in conjunction with k-means. Sparse coefficients and a space projection matrix can be simultaneously learned. The global structures and local neighborhood properties are well captured in the learning procedures. Both the processes of clustering and dimensionality reduction are realized at the same time. The notions of clustering, dimensionality reduction, low-rank representation, and local property preservation are seamlessly integrated into a unified model. The limitation of error accumulation encountered in the previous two-stage clustering framework involving low-rank representation can be alleviated. This is the first attempt to introduce both the global and local geometrical structures into k-means directly, as well L2,1-norm is used as a basic metric instead of the conventional F-norm to further improve the robustness and interpretation of the model. The superiority of the proposed RCLR method is demonstrated by extensive experiments completed on various well-known benchmark datasets.

Automatically prioritizing software development tasks extracted from codes could provide significant technical and organizational advantages. Tools exist for the automatic extraction of tasks, but they still lack the ability to capture their mutual dependencies; hence, the capability to prioritize them. Solving this important puzzle is the goal of the presented industrial challenge.

Simple detection of bugs, defects or anomalies during software development is not enough - it is necessary to apply corrective actions to eliminate them. To find out whether an anomaly exists in any software, we can measure the quality attributes using software metrics. The main goal of this paper was to find out and explain how to meaningfully attribute metrics to useful corrective actions.

In system modeling arises a fundamental question about the level of difficulty one may encounter when designing a model on a basis of some training data. In this study, we advocate that such level of difficulty inherently depends upon the variability of the available function (data). If for a pair of input data which exhibits small differences, the differences of the corresponding outputs are substantial then building a model in the presence of such data becomes more challenging than in cases of data where the differences in the output data are far more limited. Dwelling on this observation, we introduce a variability index quantifying the nature of data in terms of variability observed in input and output data, respectively. The proposed index is model-neutral (model agnostic), namely describes and quantifies the modeling challenge implied by the data irrespectively of the specific model to be constructed. In case of functions, we show that the Lipschitz constant plays a similar role as the variability index computed for experimental data. An original way of reducing values of the variability index through a nonlinear transformation of original data completed by a fuzzy rule-based model is introduced. It is shown that such rule-based architecture gives rise to a piecewise linear transformation (multipoint linear approximation) exhibiting required contraction-dilation characteristics. The optimization of this transformation is carried out with the use of a Particle Swarm Optimization algorithm. We also demonstrate that the index can be used to quantify a concept of adversarial data. Along this line, we introduce a granular characterization of adversarial feature of individual data points. A series of experiments is provided to offer a thorough illustration and detailed insight into the nature and a thorough characterization of publicly available data.

Utility pattern mining is a branch of data mining that extracts valid patterns by considering the quantity and weight of the items. In addition, utility occupancy pattern mining, which considers the quantity, importance, and proportion of the pattern in the transaction, has been proposed. Despite this advantage, there is no utility seizing approach to handle the dynamically generated data flows. As electronics are interconnected and intelligent systems are constructed, data is generated in real-time and accumulated rapidly. Therefore, a method to read data immediately in a dynamic environment and efficiently analyze massive data is required. To overcome the limitations of the existing utility occupancy methods, we propose a novel mining approach, HUOMI, which performs quickly on an increasing database. The suggested algorithm has an optimized data structure and an improved pruning technique, which can respond to the dynamic environment promptly. To indicate the effectiveness of the proposed method, performance evaluations were conducted on real and synthetic data sets. In the experimental results, the suggested algorithm showed a better performance than the other state-of-the-art algorithms.

In industrial areas, most of databases are dynamic databases, and the volume of the databases has grown with the passage of time. Especially, pattern mining for incremental database needs different approaches from static database because the profit or the accuracy of the previously inserted data can be reduced. Since data is time- sensitive, the recent data has a relatively higher value than the old data. In this paper, we suggest the damped window based average utility driven data analytics for intelligent systems, which the damped window reflects the importance according to the arrival time of the transactions. The proposed mining approach adopts novel data structure, which modify the importance of item as the passage of time, and it improves mining efficiency with several pruning strategies and without generating candidate patterns. To evaluate the performance of the proposed mining approach, we conducted various experiments using several real and synthetic data sets. The result of the experiments presented that the suggested method performs better in terms of runtime and memory usage than the other state-of-the-art mining techniques. Moreover, through the scalability experiments, which changed the number of different items or transactions, we verified that the proposed algorithm maintained a stable performance under various environmental changes.

Dual hesitant fuzzy elements (DHFEs) are suitable to express hesitant possible preferred and nonpreferred judgments of decision makers. Preference relation is an important tool in decision making that only needs the decision makers to compare a pair of objects at one time. This study focuses on decision making with dual hesitant fuzzy preference relations (DHFPRs). Considering the consistency, an additive consistency concept is defined. Meanwhile, the property of the new concept is studied. Using this consistency concept, a method for assessing the additive consistency of DHFPRs is offered. To extend the application of DHFPRs, a programming model to determine the missing DHFEs in incomplete DHFPRs is built, which have the highest additive consistency level for the known ones. Two equivalent methods to calculate the priority vector are offered. One method obtains the probabilistic dual hesitant fuzzy priority vector, and the other derives the intuitionistic fuzzy priority vector. Furthermore, a consensus index is defined to measure the consensus of individual opinions in group decision making (GDM), and an interactive method for increasing the consensus level is offered. On the basis of the additive consistency and consensus, an algorithm to GDM with DHFPRs is offered that can address inconsistent and incomplete cases. Finally, a practical example about evaluating color TV is provided to demonstrate the usefulness of the new procedure.

In practical decision-making problems, the coexistence of several complex situations increases the difficulty for decision makers to make reasonable decision, such as attributes outnumber alternatives, heterogeneous relationships among multiple attributes, and individual risk tendency of decision maker. In view of the advantage of probabilistic linguistic term sets (PLTSs) in presenting qualitative information, a novel decision-making approach with PLTSs is constructed to deal with the above special situations simultaneously. To realize this goal, some basic models have been proposed. First of all, to truly reflect the importance of attributes from the heterogeneous relationships, a weight determination model with generalized Banzhaf values is developed to analyze the interaction between combinations of attributes. Then, for analyzing the individual risk tendency of decision maker, the generalized Banzhaf TODIM method with PLTSs is constructed. Moreover, based on the above research results, the generalized Banzhaf TODIM-QUALIFLEX method with PLTSs is developed to solve decision-making problems where the number of attributes exceeds the number of alternatives, the combinations of attributes are interacted with each other, and decision maker is affected by individual risk propensity. Lastly, smartphones selection through online ratings is a typical case of decision-making problems with the above situations, which is designed to illustrate the performance of the proposed method. And its rationality and advantages are further demonstrated through some comparative analyses with other methods.

Databases that deal with the real world have various characteristics. New data is continuously inserted over time without limiting the length of the database, and a variety of information about the items constituting the database is contained. Recently generated data has a greater influence than the previously generated data. These are called the time-sensitive non-binary stream databases, and they include databases such as web-server click data, market sales data, data from sensor networks, and network traffic measurement. Many high utility pattern mining and stream pattern mining methods have been proposed so far. However, they have a limitation that they are not suitable to analyze these databases, because they find valid patterns by analyzing a database with only some of the features described above. Therefore, knowledge-based software about how to find meaningful information efficiently by analyzing databases with these characteristics is required. In this article, we propose an intelligent information system that calculates the influence of the insertion time of each batch in a large-scale stream database by applying the sliding window model and mines recent high utility patterns without generating candidate patterns. In addition, a novel list-based data structure is suggested for a fast and efficient management of the time-sensitive stream databases. Moreover, our technique is compared with state-of-the-art algorithms through various experiments using real datasets and synthetic datasets. The experimental results show that our approach outperforms the previously proposed methods in terms of runtime, memory usage, and scalability.

As a useful information representation tool, hesitant fuzzy linguistic term set (HFLTS) allows decision makers (DMs) to express their cognitive preferences in terms of several ordered and continuous linguistic terms. Considering the fact that much valuable information related to the cognitive behavior of DMs is hidden in the original evaluation information, this paper studies how to comprehensively mine uncertain information from original hesitant fuzzy linguistic evaluation information given by DMs. To address this objective, we present a new representation tool, normal wiggly hesitant fuzzy linguistic term set (NWHFLTS), which not only retains the original evaluation information, but also delivers and quantifies potential uncertain information, and can also help DMs express their evaluation information in a more complete manner. First, we develop the basic operations, score function, and comparison rule of NWHFLTS based on linguistic scale functions (LSFs), and propose the projection measure, the normal projection measure, and the normalized projection-based distance measure to describe the degree of deviation between two NWHFLTSs. Furthermore, for the case when the attribute weight is completely unknown, we combine the multiattributive border approximation area comparison (MABAC) method and develop a new method called as normal wiggly hesitant fuzzy linguistic projection-based MABAC to solve the multiattribute decision-making problems where attribute values are expressed in the form of NWHFLTS. Finally, through a practical example of marine ecological security situation, the specific calculation steps of this method are exemplified, the feasibility and advancement of the proposed method are demonstrated via a comprehensive comparative study.

Encryption alone is not enough to protect data privacy, because access pattern leaks some sensitive information. Oblivious RAM (ORAM), the solution to this problem, is still far from practical deployment for heavy storage and communication/computation overhead. To reduce them, an insightful idea was proposed to utilize non-colluding clouds to shift client computation and client-cloud communication to the clouds. The proposed multi-cloud ORAM achieved O(1) client-cloud bandwidth cost and removed most of client computation. In this paper, we exploit “disconnected ORAMoperation” and design “two-layerencryption” to further reduce these overheads. Experiments show that our proposed scheme, NewMCOS, significantly reduces evict cache size from GB/MB to KB level with about 2-3 times lower response time and 20 percent savings in bandwidth for clouds, compared to other schemes. Theoretically speaking, we reduce evict cache size from O(√N) to O(ZK), where N is the number of real data blocks, K is the number of clouds (2 <; K <; <; √N ), and Z is the number of real blocks uploaded from the client for eviction. By employing “lazy eviction operation”, the write frequency is reduced by O(Z), the shuffling bandwidth cost is reduced by Ω(Z log Z). Meanwhile, NewMCOS is proved to be secure.

Shadowed sets provide a meaningful description of information granules by abstracting the corresponding fuzzy sets into three categories: full acceptance, full rejection, and uncertain (represented by shadows). One of the main motivating points to derive shadowed sets from fuzzy sets is the determination and explanation of the separation thresholds based on a specific optimization mechanism. The available optimization objective functions are mainly discussed on semantic interpretations and their mathematical properties; constructive algorithms for optimal solutions have rarely been reported. In this paper, the continuous and convex properties of Pedrycz's optimization objective function to construct shadowed sets, as well as the existence and uniqueness of solution points, are analyzed in detail. It is demonstrated that different approximation region partitions would be generated even under the same optimization model, which requires further criteria to make the constructed shadowed sets well-defined. To address this limitation, the notions of passive and active constrained shadowed sets are introduced. A fast algorithm to obtain the proposed constrained shadowed sets is also designed based on the analyzed mathematical properties. Its performance is then illustrated by some typical fuzzy sets and some real data from the UCI repository.

The key issue of determining a suitable (feasible) number of clusters still remains open. This paper proposes a graph-theoretic clustering iterative algorithm that employs a novel idea of using noise and information associated with it to determine clusters. The proposed method does not require any parameters whose values have to be supplied by the user. A series of experiments reported in the study show that the proposed algorithm can extract significant cluster information even in case of complicated geometry of data sets.

Incomplete data clustering is often encountered in practice. Here the treatment of missing attribute value and the optimization procedure of clustering are the important factors impacting the clustering performance. In this study, a missing attribute value becomes an information granule and is represented as a certain interval. To avoid intervals determined by different cluster information, we propose a congeneric nearest-neighbor rule-based architecture of the preclassification result, which can improve the effectiveness of estimation of missing attribute interval. Furthermore, a global fuzzy clustering approach using particle swarm optimization assisted by the Fuzzy C-Means is proposed. A novel encoding scheme where particles are composed of the cluster prototypes and the missing attribute values is considered in the optimization procedure. The proposed approach improves the accuracy of clustering results, moreover, the missing attribute imputation can be implemented at the same time. The experimental results of several UCI data sets show the efficiency of the proposed approach.

In this paper, a fuzzy c-means clustering algorithm based on interval-valued weights is proposed for improving clustering performance. In the proposed algorithm, the interval-valued weights are first constructed by synergy of the ReliefF algorithm and the analytic hierarchy process (AHP) method, and then they are transformed into a constraint condition associating with each weight variable in the weighted clustering objective function. In the sequence, the weighted clustering objective function is solved by combining the Lagrange multiplier method with the gradient-based iteration computation. In the whole process of algorithm iteration, a compulsion strategy with human–computer cooperation is adopted to ensure each weight variable satisfies interval constraint itself. Three well-known data set are used to perform profound experiments. Experimental results clearly show that the proposed algorithm has better clustering performance than other the weighted fuzzy c-means clustering algorithm.

In decision analysis, uncertainty is usually described in the framework of probability. However, a large number of experimental and theoretical studies showed that a single nature of probability does not accurately capture human preferences. To avoid this drawback, they use imprecise probabilities. But, as decision maker is usually uncertain about first-order imprecise probabilities, imprecise hierarchical probability models are used. For most of such models, the second levels are precise. There also exist studies on two-level imprecise hierarchical models, which use imprecise probabilities or possibilities at the second level. Most of these works are based on lower prevision theory leading to a large number of optimization problems. In the present paper, we propose an imprecise hierarchical decision-making model where the first and the second level are described by interval probabilities. The method associates with the construction of a nonadditive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function.

Semi-supervised learning is one of the important topics in machine learning, concerning with pattern classification where only a small subset of data is labeled. In this paper, a new network-based (or graph-based) semi-supervised classification model is proposed. It employs a combined random-greedy walk of particles, with competition and cooperation mechanisms, to propagate class labels to the whole network. Due to the competition mechanism, the proposed model has a local label spreading fashion, i.e., each particle only visits a portion of nodes potentially belonging to it, while it is not allowed to visit those nodes definitely occupied by particles of other classes. In this way, a “divide-and-conquer” effect is naturally embedded in the model. As a result, the proposed model can achieve a good classification rate while exhibiting low computational complexity order in comparison to other network-based semi-supervised algorithms. Computer simulations carried out for synthetic and real-world data sets provide a numeric quantification of the performance of the method.

Kernel machines and rough sets are two classes of commonly exploited learning techniques. Kernel machines enhance traditional learning algorithms by bringing opportunities to deal with nonlinear classification problems, rough sets introduce a human-focused way to deal with uncertainty in learning problems. Granulation and approximation play a pivotal role in rough sets-based learning and reasoning. However, a way how to effectively generate fuzzy granules from data has not been fully studied so far. In this study, we integrate kernel functions with fuzzy rough set models and propose two types of kernelized fuzzy rough sets. Kernel functions are employed to compute the fuzzy T-equivalence relations between samples, thus generating fuzzy information granules in the approximation space. Subsequently fuzzy granules are used to approximate the classification based on the concepts of fuzzy lower and upper approximations. Based on the models of kernelized fuzzy rough sets, we extend the measures existing in classical rough sets to evaluate the approximation quality and approximation abilities of the attributes. We discuss the relationship between these measures and feature evaluation function ReliefF, and augment the ReliefF algorithm to enhance the robustness of these proposed measures. Finally, we apply these measures to evaluate and select features for classification problems. The experimental results help quantify the performance of the KFRS.

Regression models are well known and widely used as one of the important models in system modeling. In this paper, we extend the concept of regression models in order to handle hybrid data coming from various sources of data quite often exhibiting diverse levels of quality. The major objective of this study is to develop a convex hull method being regarded as a potential vehicle, which helps reduce the computing time, especially in real-time data analysis as well as an overall computational complexity. We propose an efficient real-time fuzzy switching regression analysis based on the convex hull approach in which a Beneath-Beyond algorithm is employed to design a convex hull. The method addresses situations when we have to deal with heterogeneous data. In the proposed design setting, we emphasize a pivotal role of convex hull approach which is crucial when alleviating limitations of a linear programming manifesting in system modeling.

In this study, we discuss a concept of shadowed sets and present their applications. To establish some sound compromise between the qualitative Boolean (two-valued) description of data and quantitative membership grades, we introduce an interpretation framework of shadowed sets. Shadowed sets are discussed as three-valued constructs induced by fuzzy sets assuming three values (that could be interpreted as full membership, full exclusion, and uncertain membership). The algorithm of converting membership functions into this quantification is a result of a certain optimization problem guided by the principle of uncertainty localization. We revisit fundamental ideas of relational calculus in the setting of shadowed sets. We demonstrate how shadowed sets help in problems in data interpretation in fuzzy clustering by leading to the three-valued quantification of data structure that consists of core, shadowed, and uncertain structure. © 2008 Wiley Periodicals, Inc.

The notion of a rough set was originally proposed by Pawlak underwent a number of extensions and generalizations. Dubois and Prade (1990) introduced fuzzy rough sets which involve the use of rough sets and fuzzy sets within a single framework. Radzikowska and Kerre (2002) proposed a broad family of fuzzy rough sets, referred to as ( t)-fuzzy rough sets which are determined by some implication operator (implicator), and a certain t-norm. In order to describe the linguistically represented concepts coming from data available in some information system, the concept of fuzzy rough sets are redefined and further studied in the setting of the Axiomatic Fuzzy Set (AFS) theory. Compared with the ( t)-fuzzy rough sets, the advantages of AFS fuzzy rough sets are twofold. They can be directly applied to data analysis present in any information system without resorting to the details concerning the choice of the implication, t-norm and a similarity relation S. Furthermore such rough approximations of fuzzy concepts come with a well-defined semantics and therefore offer a sound interpretation. Some examples are included to illustrate the effectiveness of the proposed construct. It is shown that the AFS fuzzy rough sets provide a far higher flexibility and effectiveness in comparison with rough sets and some of their generalizations.

Accurate classification of biomedical spectra is often difficult due to the large number of features, which tends to have a confounding effect. We present a strategy where the original spectral feature space is transformed using a fuzzy set theoretic method, which analyzes the features' interquartile ranges, coupled with a stochastic feature selection mechanism, which identifies highly discriminatory feature subsets. We demonstrate the effectiveness of this strategy using biofluid data acquired from a magnetic resonance spectrometer

Web information may currently be acquired by activating search engines. However, our daily experience is not only that web pages are often either redundant or missing but also that there is a mismatch between information needs and the web's responses. If we wish to satisfy more complex requests, we need to extract part of the information and transform it into new interactive knowledge. This transformation may either be performed by hand or automatically. In this article we describe an experimental agent-based framework skilled to help the user both in managing achieved information and in personalizing web searching activity. The first process is supported by a query-formulation facility and by a friendly structured representation of the searching results. On the other hand, the system provides a proactive support to the searching on the web by suggesting pages, which are selected according to the user's behavior shown in his navigation activity. A basic role is played by an extension of a classical fuzzy-clustering algorithm that provides a prototype-based representation of the knowledge extracted from the web. These prototypes lead both the proactive suggestion of new pages, mined through web spidering, and the structured representation of the searching results. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1101–1122, 2007.

Fuzzy neurons may have outstanding learning abilities and are endowed with significant interpretation capabilities. In this study, we are concerned with the development of logic networks composed of fuzzy neurons. The main phase of the design includes the granulation of the output space (via triangular fuzzy sets) being realized with the use of fuzzy equalization. In the sequel these fuzzy sets are used to guide the construction of a family of fuzzy sets in the input space. Further processing of the resulting fuzzy sets deals with some additional aggregation of those that are not sufficiently distinct. This helps reduce the size of the logic network. We include comprehensive experimentation and offer a thorough interpretation of the networks. Experiments concerning real-world continuous data help evaluate the network's appealing properties: transparent interpretability and practical feasibility. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 1249–1267, 2006.

Abstract The explosive growth of the Web and the consequent exigency of the Web personalization domain have gained a key position in the direction of customization of the Web information to the needs of specific users, taking advantage of the knowledge acquired from the analysis of the user's navigational behavior (usage data) in correlation with other information collected in the Web context, namely, structure, content, and user profile data. This work presents an agent‐based framework designed to help a user in achieving personalized navigation, by recommending related documents according to the user's responses in similar‐pages searching mode. Our agent‐based approach is grounded in the integration of different techniques and methodologies into a unique platform featuring user profiling, fuzzy multisets, proximity‐oriented fuzzy clustering, and knowledge‐based discovery technologies. Each of these methodologies serves to solve one facet of the general problem (discovering documents relevant to the user by searching the Web) and is treated by specialized agents that ultimately achieve the final functionality through cooperation and task distribution.

Fuzzy reasoning is intensively used in intelligent systems including fuzzy control, classification, expert systems, and networks to name a few dominant categories of such architectures. As being a fundamental construct permeating so many diverse areas, fuzzy reasoning was studied with respect to its fundamental properties such as robustness. The notion of robustness or sensitivity becomes of paramount importance by leading to a more comprehensive understanding of the way in which reasoning processes are developed. In this study, we introduce and study properties of some measures of robustness (or sensitivity) of fuzzy connectives and implication operators and discuss their relationships with perturbation properties of fuzzy sets. The results produced here are compared and contrasted with the previous findings available in the literature. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 393–413, 2005.

We discuss a problem of synthesis and analysis of rules based on experimental numeric data. Two descriptors of the rules that are viewed individually and en block are introduced. The coverage of the rules is quantified in terms of the data being covered by the antecedents and conclusions standing in the rule. Although this index describes each rule individually, the consistency of the rule deals with the quality of the rule viewed compared with other rules. It expresses how much the rule “interacts” with others in the sense that its conclusion is affected (distorted) by the conclusion parts coming from other rules. We propose a synthetic index of rule relevance that combines the two already introduced descriptors. We show how the rules are formed by means of fuzzy clustering and their quality is evaluated by means of the aforementioned indexes. Global characteristics of a set of rules also are discussed and related to the number of information granules formed in the space of antecedents and conclusions. Finally, we discuss the rules in the setting of granular modeling and express their performance in the design of numeric models. © 2004 Wiley Periodicals, Inc.

In this study, we propose a hybrid identification algorithm for a class of fuzzy rule-based systems. The rule-based fuzzy modeling concerns structure optimization and parameter identification using the fuzzy inference methods and hybrid structure combined with two methods of optimization theories for nonlinear systems. Two types of inference methods of a fuzzy model concern a simplified and linear type of inference. The proposed hybrid optimal identification algorithm is carried out using a combination of genetic algorithms and an improved complex method. The genetic algorithms determine initial parameters of the membership function of the premise part of the fuzzy rules. In the sequel, the improved complex method (being in essence a powerful auto-tuning algorithm) leads to fine-tuning of the parameters of the respective membership functions. An aggregate performance index with a weighting factor is proposed in order to achieve a balance between performance of the fuzzy model obtained for the training and testing data. Numerical examples are included to evaluate the performance of the proposed model. They are also contrasted with the performance of the fuzzy models existing in the literature. © 2002 John Wiley & Sons, Inc.

The theory of shadowed sets is one among several key contributors to the area of granular computing. As the name stipulates, granular computing embraces processing of information granules. By information granules we mean collections of entities being assembled together in order to achieve a certain conceptual and/or computational feasibility of processing carried out in any complex system, no matter whether natural or artificial. Granular computing, as being exclusively geared toward processing of information granules, subsumes the commonly encountered numeric style of processing. The intent of shadowed sets is to capture (“isolate” or “localize”) and quantify the factor of uncertainty inherently existing in any real-world system. We first discuss the underlying theoretical underpinnings of shadowed sets that primarily dwell on the pillar of three-valued logic. We also come up with a number of illustrative examples that help grasp the essence of the concept. The study embarks on a variety of the applications of shadowed sets to fuzzy mappings along with an analysis of their relevance as well as data quantization. In the case of fuzzy mappings, it is revealed that shadowed sets provide an interesting three-valued quantification of the property of relevancy (such as acceptable mapping, marginal mapping, and a lack of mapping). This article includes a number of detailed calculations concerning two commonly exploited classes of triangular and Gaussian fuzzy sets. Moreover, we elaborate on the exploration of shadowed sets as an algorithmic realization of the least commitment principle advocated by Marr. © 2002 John Wiley & Sons, Inc.

Defuzzification is an important operation in the theory of fuzzy sets. It transforms a fuzzy set information into a numeric data information. This operation along with the operation of fuzzification is critical to the design of fuzzy systems as both of these operations provide nexus between the fuzzy set domain and the real-valued scalar domain. We need the synergy of both of these domains to solve many of our ill-posed problems effectively. In this paper, we address the problem of defuzzification, we present merits and demerits of various defuzzification strategies that are used in the theory and practice, and in design and implementation of applications involving fuzzy theory, fuzzy control, and fuzzy rule base, and fuzzy inference-based systems. We also present in this paper a simple and yet a novel defuzzification mechanism. © 2001 John Wiley & Sons, Inc.

In this study, we introduce a concept of granular worlds and elaborate on various representation and communication issues arising therein. A granular world embodies a collection of information granules being regarded as generic conceptual entities used to represent knowledge and handle problem solving. Granular computing is a paradigm supporting knowledge representation, coping with complexity, and facilitating interpretation of processing. In this sense, it is crucial to all man-machine pursuits and data mining and intelligent data analysis, in particular. There are two essential facets that are inherently associated with any granular world, that is a formalism used to describe and manipulate information granules and the granularity of the granules themselves (roughly speaking, by the granularity we mean a “size” of such information granules; its detailed definition depends upon the formal setting of the granular world). There are numerous formal models of granular worlds ranging from set-theoretic developments (including sets, fuzzy sets, and rough sets) to probabilistic counterparts (random sets, random variables and alike). In light of the evident diversity of granular world (occurring both in terms of the underlying formal settings as well as levels of granularity), we elaborate on their possible interaction and identify implications of such communication. More specifically, we have cast these in the form of the interoperability problem that is associated with the representation of information granules. © 2000 John Wiley & Sons, Inc.

This study elaborates on the role of information granularity in the development of fuzzy controllers. As opposed to numeric data being commonly accepted by fuzzy controllers, we discuss a general processing framework involving data-information granules exhibiting various levels of information granularity. The paper analyzes an impact of information granularity on the performance of the controller. We study a way in which information granules arise in control problems, elaborate on a way of describing these granules as well as provide a way of quantifying the level of information granularity. A number of analysis and design issues are studied including robustness of the fuzzy controller, representation of linguistic information and quantification of its granularity. Nonlinear characteristics of the compiled version of the fuzzy controller operating in presence of granular information are discussed in detail. Illustrative numerical examples are provided as well. ©1999 John Wiley & Sons, Inc.

This paper considers the construction of Petri nets to simulate the computation performed by decision systems. Algorithms are given to construct Petri nets which correspond to decision rules, information systems, and real-time decision systems. Rough as well as rough fuzzy Petri net extensions of colored and generalized fuzzy Petri nets are used to create highly parallel programs to simulate reasoning system computations. Constructed nets make it possible to evaluate the design of decision system tables, and to trace computations in rules derived from decision tables. Start places of nets are connected to Dill process receptors which await input from the environment. Time consumption during the propagation of outputs from sensors in a decision system is monitored with timers called approximate time windows, which measure durations between firings of decision transitions relative to time granules with names such as early, ontime, and late. Guards on decision transitions are propositional functions which permit a rule to fire for some sensor values and not for others. In addition, the design of guards makes allowance for multivalued logic, where conditional sensor readings are assessed in terms of their degree of membership in sensor measurement granules. In some cases, a rule can fire if the degree of truth of its guard (premise) is above some threshold. Through simulation, designers can arrive at reasonable estimates of the period of timers on decision transitions. The approach to simulating computations by decision systems presented in this paper results in fast, massively parallel programs implementable on a multiprocessor. © 1999 John Wiley & Sons, Inc.

In this paper we introduce the use of contextual transformation functions to adjust membership functions in fuzzy systems. We address both linear and nonlinear functions to perform linear or nonlinear context adaptation, respectively. The key issue is to encode knowledge in a standard frame of reference, and have its meaning tuned to the situation by means of an adequate transformation reflecting the influence of context in the interpretation of a concept. Linear context adaptation is simple and fast. Nonlinear context adaptation is more computationally expensive, but due to its nonlinear characteristic, different parts of base membership functions can be stretched or expanded to best fit the desired format. Here we use a genetic algorithm to find a nonlinear transformation function, given the base membership functions and a set of data extracted from the environment classified by means of fuzzy concepts. © 1998 John Wiley & Sons, Inc.

Proposed is a certain generalization of nonmonotonic fuzzy set operators introduced originally by R. R. Yager. By introducing a modulating function one can effectively model situations in which available information interacts (overlaps) with a given default fuzzy set. Discussed is a complete learning environment in which the default values (sets) can be derived based upon some experimental data. The role of the nonmonotonic operations is also revealed in the setting of reasoning carried out in the presence of fuzzy data. ©1997 John Wiley & Sons, Inc.

Concept formation contrives one among vital issues in all fields of science. It can be stated that, to a significant degree, a scientific discovery is related to various aspects of creation of general categories out of a mass of raw empirical data analyzed from a suitable perspective. Thus, as it is seen now, the concept of any notion is constructed on the basis of a significant amount of previous experience. Despite a lot of research completed, there still exists a number of open questions about diverse features of the constructed concepts. In this article we develop a framework for concept formation making use of a logical platform of fuzzy sets combined with mechanisms of neurocom-putations. It will be indicated how for a given naming of the concept its description can be derived. Moreover, a particular attention will be devoted to mechanisms justifying a relevance of the concepts with respect to a collection of available empirical facts. This may play a primordial role in recognizing some limitations of a character of the concept (i.e., its generality or specificity) which cannot be exceeded simultaneously not losing consistency with the family of collected objects utilized within the process of concept formation.

The article concentrates on selected aspects of knowledge representation. It is considered how fuzzy sets viewed as linguistic labels (information granules) determine a representation frame. the representation scheme is discussed with respect to its perception level and a scope of individual labels. Both the features can be handled by fuzzy sets and easily modeled by changing associated parameters of corresponding membership functions. Problems of prototype determination in the original space (in which the objects are characterized) as well as in the space of linguistic labels are studied. It is argued that the space of grades of membership functions is more suitable to capture a notion of the prototype. Different aspects of matching are also brought into account.