Fuzzy Cognitive Mapping (FCM) and the extensive family of models derived from it have firmly established their strong position in the landscape of machine learning algorithms. Specifically designed for pattern classification and multi-output regression, the recently introduced Recurrence-aware Long-term Cognitive Network (r-LTCN) model is one of these FCM-inspired extensions. On the one hand, this recurrent neural network connects all temporal states generated during the reasoning process with the decision-making layer. On the other hand, it uses a quasi-nonlinear reasoning rule devoted to avoiding convergence issues caused by unique fixed points, which typically emerge in other FCM models. In the original paper, the authors employed a combination of unsupervised and supervised learning to compute the r-LTCNs’ learnable parameters. Despite r-LTCNs’ astounding performance for a wide variety of pattern classification problems, the literature reports no attempt to train these recurrent neural systems in a fully supervised manner nor provide insights into their performance in other machine learning settings. This paper brings forward a modified Backpropagation Through Time learning (BPTT) algorithm devoted to training r-LTCN models used for multi-output regressions tasks rather than pattern classification. The proposed BPPT includes a simple yet effective mechanism to deal with the vanishing gradient within the recurrent layer that operates as a closed system while being tailored to the quasi-nonlinear reasoning mechanism. Empirical evaluation of the proposed BPTT algorithm using 20 multi-output regression problems reveals that it produces lower prediction errors compared with other state-of-the-art learning approaches.

Nowadays, a large amount of structured and unstructured data is being produced in various fields, creating tremendous opportunities to implement Machine Learning (ML) algorithms for decision-making. Although ML algorithms can outperform human performance in some fields, the black-box inherent characteristics of advanced models can hinder experts from exploiting them in sensitive domains such as medicine. The black-box nature of advanced ML models shadows the transparency of these algorithms, which could hamper their fair and robust performance due to the complexity of the algorithms. Consequently, individuals, organizations, and societies will not be able to achieve the full potential of ML without establishing trust in its development, deployment, and use. The field of eXplainable Artificial Intelligence (XAI) endeavors to solve this problem by providing human-understandable explanations for black-box models as a potential solution to acquire trustworthy AI. However, explainability is one of many requirements to fulfill trustworthy AI, and other prerequisites must also be met. Hence, this survey analyzes the fulfillment of five algorithmic requirements of accuracy, transparency, trust, robustness, and fairness through the lens of the literature in the medical domain. Regarding that medical experts are reluctant to put their judgment aside in favor of a machine, trustworthy AI algorithmic fulfillment could be a way to convince them to use ML. The results show there is still a long way to implement the algorithmic requirements in practice, and scholars need to consider them in future studies.

The paper presents the presumably correct decision sets as a tool to analyze uncertainty in the form of inconsistency in decision systems. As a first step, problem instances are gathered into three regions containing weak members, borderline members, and strong members. This is accomplished by using the membership degrees of instances to their neighborhoods while neglecting their actual labels. As a second step, we derive the presumably correct and incorrect sets by contrasting the decision classes determined by a neighborhood function with the actual decision classes. We extract these sets from either the regions containing strong members or the whole universe, which defines the strict and relaxed versions of our theoretical formalism. These sets allow isolating the instances difficult to handle by machine learning algorithms as they are responsible for inconsistent patterns. The simulations using synthetic and real-world datasets illustrate the advantages of our model compared to rough sets, which is deemed a solid state-of-the-art approach to cope with inconsistency. In particular, it is shown that we can increase the accuracy of selected classifiers up to 36% by weighting the presumably correct and incorrect instances during the training process.

Machine-learning solutions for pattern classification problems are nowadays widely deployed in society and industry. However, the lack of transparency and accountability of most accurate models often hinders their safe use. Thus, there is a clear need for developing explainable artificial intelligence mechanisms. There exist model-agnostic methods that summarize feature contributions, but their interpretability is limited to predictions made by black-box models. An open challenge is to develop models that have intrinsic interpretability and produce their own explanations, even for classes of models that are traditionally considered black boxes like (recurrent) neural networks. In this article, we propose a long-term cognitive network (LTCN) for interpretable pattern classification of structured data. Our method brings its own mechanism for providing explanations by quantifying the relevance of each feature in the decision process. For supporting the interpretability without affecting the performance, the model incorporates more flexibility through a quasi-nonlinear reasoning rule that allows controlling nonlinearity. Besides, we propose a recurrence-aware decision model that evades the issues posed by the unique fixed point while introducing a deterministic learning algorithm to compute the tunable parameters. The simulations show that our interpretable model obtains competitive results when compared to state-of-the-art white and black-box models.

Machine Learning (ML) models play an important role in healthcare thanks to their remarkable performance in predicting complex phenomena. During the COVID-19 pandemic, different ML models were implemented to support decisions in the medical settings. However, clinical experts need to ensure that these models are valid, provide clinically useful information, and are implemented and used correctly. In this vein, they need to understand the logic behind the models to be able to trust them. Hence, developing transparent and interpretable models has increasing relevance. In this work, we applied four interpretable ML models including logistic regression, decision tree, pyFUME, and RIPPER to classify suspected COVID-19 patients based on clinical data collected from blood samples. After preprocessing the data set and training the models, we evaluate the models based on their predictive performance. Then, we illustrate that interpretability can be achieved in different ways. First, SHAP explanations are built from logistic regression and decision trees to obtain the features' importance. Then, the potential of pyFUME and RIPPER in providing inherent interpretability are reflected. Finally, potential ways to achieve trust in future studies are briefly discussed.

This paper presents a Fuzzy Cognitive Map model to quantify implicit bias in structured datasets where features can be numeric or discrete. In our proposal, problem features are mapped to neural concepts that are initially activated by experts when running what-if simulations, whereas weights connecting the neural concepts represent absolute correlation/association patterns between features. In addition, we introduce a new reasoning mechanism equipped with a normalization-like transfer function that prevents neurons from saturating. Another advantage of this new reasoning mechanism is that it can easily be controlled by regulating nonlinearity when updating neurons’ activation values in each iteration. Finally, we study the convergence of our model and derive analytical conditions concerning the existence and unicity of fixed-point attractors.

Abstract In this paper, we present a recurrent neural system named long short-term cognitive networks (LSTCNs) as a generalization of the short-term cognitive network (STCN) model. Such a generalization is motivated by the difficulty of forecasting very long time series efficiently. The LSTCN model can be defined as a collection of STCN blocks, each processing a specific time patch of the (multivariate) time series being modeled. In this neural ensemble, each block passes information to the subsequent one in the form of weight matrices representing the prior knowledge. As a second contribution, we propose a deterministic learning algorithm to compute the learnable weights while preserving the prior knowledge resulting from previous learning processes. As a third contribution, we introduce a feature influence score as a proxy to explain the forecasting process in multivariate time series. The simulations using three case studies show that our neural system reports small forecasting errors while being significantly faster than state-of-the-art recurrent models.

Fuzzy-rough cognitive networks (FRCNs) are recurrent neural networks (RNNs) intended for structured classification purposes in which the problem is described by an explicit set of features. The advantage of this granular neural system relies on its transparency and simplicity while being competitive to state-of-the-art classifiers. Despite their relative empirical success in terms of prediction rates, there are limited studies on FRCNs' dynamic properties and how their building blocks contribute to the algorithm's performance. In this article, we theoretically study these issues and conclude that boundary and negative neurons always converge to a unique fixed-point attractor. Moreover, we demonstrate that negative neurons have no impact on the algorithm's performance and that the ranking of positive neurons is invariant. Moved by our theoretical findings, we propose two simpler fuzzy-rough classifiers that overcome the detected issues and maintain the competitive prediction rates of this classifier. Toward the end, we present a case study concerned with image classification, in which a convolutional neural network is coupled with one of the simpler models derived from the theoretical analysis of the FRCN model. The numerical simulations suggest that once the features have been extracted, our granular neural system performs as well as other RNNs.

Semi-supervised classifiers combine labeled and unlabeled data during the learning phase in order to increase classifier's generalization capability. However, most successful semi-supervised classifiers involve complex ensemble structures and iterative algorithms which make it difficult to explain the outcome, thus behaving like black boxes. Furthermore, during an iterative self-labeling process, mistakes can be propagated if no amending procedure is used. In this paper, we build upon an interpretable self-labeling grey-box classifier that uses a black box to estimate the missing class labels and a white box to make the final predictions. We propose a Rough Set based approach for amending the self-labeling process. We compare its performance to the vanilla version of our self-labeling grey-box and the use of a confidence-based amending. In addition, we introduce some measures to quantify the interpretability of our model. The experimental results suggest that the proposed amending improves accuracy and interpretability of the self-labeling grey-box, thus leading to superior results when compared to state-of-the-art semi-supervised classifiers.

In this paper, we build a recommender system based on Long-term Cognitive Networks (LTCNs), which are a type of recurrent neural network that allows reasoning with prior knowledge structures. Given that our approach is context-free and that we did not involve human experts in our study, the prior knowledge is replaced with Pearson’s correlation coefficients. The proposed architecture expands the LTCN model by adding Gaussian kernel neurons that compute estimates for the missing ratings. These neurons feed the recurrent structure that corrects the estimates and makes the predictions. Moreover, we present an extension of the non-synaptic backpropagation algorithm to compute the proper non-linearity of each neuron together with its activation boundaries. Numerical results using several case studies have shown that our proposal outperforms most state-of-the-art methods. Towards the end, we explain how can we inject expert knowledge to the proposed neural system.

After 30 years of research, challenges and solutions, Fuzzy Cognitive Maps (FCMs) have become a suitable knowledgebased methodology for modeling and simulation. This technique is especially attractive when modeling systems that are characterized by ambiguity, complexity and non-trivial causality. FCMs are well-known due to the transparency achieved during modeling tasks. The literature reports successful studies related to the modeling of complex systems using FCMs. However, the situation is not the same when it comes to software implementations where domain experts can design FCM-based systems, run simulations or perform more advanced experiments. The existing implementations are not proficient in providing many options to adjust essential parameters during the modeling steps. The gap between the theoretical advances and the development of accurate, transparent and sound FCM-based systems advocates for the creation of more complete and flexible software products. Therefore, the goal of this paper is to introduce FCM Expert, a software tool for fuzzy cognitive modeling oriented to scenario analysis and pattern classification. The main features of FCM Expert rely on Machine Learning algorithms to compute the parameters defining the model, optimize the network topology and improve the system convergence without losing information. On the other hand, FCM Expert allows performing WHAT-IF simulations and studying the system behavior through a friendly, intuitive and easy-to-use graphical user interface.

During the last decade Fuzzy Cognitive Maps (FCM) have become a useful tool for solving unstructured problems. In a few words they could be defined as Recurrent Neural Networks for simulating complex systems, where neurons denote concepts, objects or entities of the investigated system. Normally FCM are entirely designed using the best knowledge of a group of experts in a given domain, so frequently learning algorithms for tuning the model parameters are required. Despite the theoretical advances in such fields, the lack of a suitable computational framework for handling FCM-based systems is still an open problem. This paper introduces a novel tool for designing and simulating FCM which gathers several learning algorithms for adjusting the introduced parameters. More specifically, the framework includes supervised and unsupervised learning algorithms for computing the causal weights, algorithms for optimizing the network topology in large FCM (without losing significant information) and also methods for improving the global convergence on continuous FCM. It should be stated that these algorithms are oriented to prediction tasks, but they could be easily extended to other fields.

During the last couple of decades, evolutionary and swarm intelligence algorithms have significantly advanced the state of the art for both discrete and numerical optimization. Without niching strategies, they usually converge to a single optimum, even in multimodal search spaces where numerous global or local solutions exist. In the literature, several niching approaches have been proposed for simultaneously computing multiple optima, though most of them require some user-specified parameters that should be calculated a priori, i.e. additional knowledge about the problem domain is required. Recently, it was demonstrated that particle swarm optimization (PSO) using a ring topology for neighborhood definition can give rise to robust and parameterless niching methods. Nevertheless, their performance dramatically worsens when the dimensionality of the solution space hikes, thus increasing the number of local optima. This paper aims at enhancing the performance of these types of PSO-based algorithms by introducing two procedures: (1) a differential operator for improving the search ability and (2) a heuristic clearing operator for controlling the swarm diversity. Such operators are probabilistically activated through a novel self-adaptive learning strategy. Empirical results confirm the superiority of our proposed scheme with respect to six other competitive niching techniques.