Artificial intelligence (AI) systems are increasingly adopted in high‐stakes domains such as healthcare and finance, so the demand for transparency and interpretability has grown substantially. EXplainable AI (XAI) methods have emerged to address this challenge, but individual techniques often offer limited, fragmented insights. This paper introduces Meta‐explainers, a novel ensemble‐based XAI framework that integrates multiple explanation types—specifically relevance‐based and counterfactual methods—into unified, multifaceted and complementary meta‐explanations. Inspired by meta‐classification principles, our approach structures the explanation process into five stages: generation, grouping, evaluation, aggregation, and visualization. Each stage is designed to preserve the unique strengths of individual XAI techniques while enhancing their interpretability and coherence when combined. Experimental results on both image (MNIST) and tabular (Breast Cancer) datasets show that Meta‐explainers consistently outperform individual and state‐of‐the‐art ensemble explanation methods in terms of explanation quality, as measured by established metrics. This work paves the way toward more holistic and user‐centered AI explainability with a flexible methodology that can be extended to incorporate additional explanation paradigms.

Although deep learning models can solve complex prediction problems, they have been criticized for being ‘black boxes’. This implies that their decisions are difficult, if not impossible, to explain by simply inspecting their internal knowledge structures. Explainable Artificial Intelligence has attempted to open the black-box through model-specific and agnostic post-hoc methods that generate visualizations or derive associations between the problem features and the model predictions. This paper proposes a new method, termed REPROT, that explains the decisions of complex deep learning architectures based on local reducts of an image. A ‘reduct’ is a set of sufficiently descriptive features that can fully characterize the acquired knowledge. The created reducts are used to build a ‘prototype image’ that visually explains the inference obtained by a black-box model for an image. We focus on deep learning architectures whose complexity and internal particularities demand adapting existing model-specific explanation methods, making the explanation process more difficult. Experimental results show that the black-box model can detect an object using the prototype image generated from the reduct. Hence, the explanations will be given by “the minimum set of features sufficient for the neural model to detect an object”. The confidence scores obtained by architectures such as Inception, Yolo, and Mask R-CNN are higher for prototype images built from the reduct than those built from the most important superpixels according to the LIME method. Moreover, the target object is not detected on several occasions through the LIME output, thus supporting the superiority of the proposed explanation method.

Neural networks are considered a black-box model as their strength in modeling complex interactions makes its operation almost impossible to explain. Still, neural networks remain very interesting tools as they have shown promising performance in various classification tasks. Layer-wise relevance propagation is a technique that, based on a propagation approach, is able to explain the predictions obtained by a neural network. In this work, we propose four adaptations of this technique to operate on multi-label neural networks. The proposed methods provide new ways of distributing the relevance between the output layer and the preceding ones. The efficacy of these adaptations is demonstrated after an experimental study. The study is carried out based on existing evaluation criteria in the literature that measure the explanation's quality. These methods are applied to a case study in which a neural network is used to detect secondary coinfections in patients infected with SARS-CoV-2. Overall, the proposed methods provide a post-hoc interpretability stage of the results.

This paper elaborates on the modeling and simulation of complex systems involving uncertainty. More explicitly, we are interested in situations in which experts hesitate about the exact values of variables when designing the model. Such situations can be modeled using Interval-valued Long-term Cognitive Networks (IVLTCNs). In this model, the activation values and the weights between neural concepts are expressed as interval grey numbers. Unlike other grey cognitive networks, our model neither imposes restrictions on the weights nor performs a whitenization process. The second contribution of this paper is a nonsynaptic grey backpropagation algorithm, which allows adjusting the learnable parameters of IVLTCNs under uncertainty conditions. Moreover, this learning algorithm does not alter the linear knowledge representations provided by domain experts during the modeling phase.

Fuzzy cognitive maps (FCMs) are recurrent neural networks comprised of well-defined concepts and causal relations. While the literature about real-world FCM applications is prolific, the studies devoted to understanding the foundations behind these neural networks are rather scant. In this article, we introduce several definitions and theorems that unveil the dynamic behavior of FCM-based models equipped with transfer F-functions. These analytical expressions allow estimating bounds for the activation value of each neuron and analyzing the covering and proximity of feasible activation spaces. The main theoretical findings suggest that the state space of any FCM model equipped with transfer F-functions shrinks infinitely with no guarantee for the FCM to converge to a fixed point but to its limit state space. This result in conjunction with the covering and proximity values of FCM-based models helps understand their poor performance when solving complex simulation problems.

In contrast with the extense variety of machine learning algorithms, to fully automate the reasoning process, only a few can take advantage of the expert knowledge. Fuzzy Cognitive Maps (FCMs) are neural networks that can naturally integrate this kind of knowledge in the inference process. Nevertheless, FCMs have serious drawbacks difficult to overcome from the absence of an intrinsically learning algorithm or limited prediction horizon of the activation space of the neurons. Recently, some variants of the FCMs like Short-Term Cognitive Networks (STCN) and Long Term Cognitive Networks (LTCN) have been proposed to solve these problems. In this paper, we propose a new neural network model as a variant of LTCNs called Long-Term Cognitive Networks with Inputs (LTCNIs). A new kind of input neuron which is not present in the traditional FCMs approach or the derived algorithms STCNs and LTCNs is introduced, in order to model inputs like energy or mass in physical systems. The performance of the method is discussed through the modeling of a passive circuit problem. As a second contribution, a new flexible reasoning strategy, which preserves the expert knowledge through synaptic learning is presented. A synaptic learning based on a gradient descent method is implemented limited by a set of restrictions that preserves the model semantics.

Recently, a learning procedure to improve the overall convergence of sigmoid fuzzy cognitive maps used in pattern classification was proposed. The algorithm estimates the slope of each sigmoid neuron while preserving the causal weights. This paper proposes a more realistic error function for this algorithm, which is based on 1) the dissimilarity between two consecutive responses, and 2) the dissimilarity between the current output and the expected one. As a second contribution, we introduce sufficient conditions to arrive at stability features. These conditions allow assessing the accuracy-convergence tradeoff attached to the proposed learning procedure.

In a multilabel classification problem, each object gets associated with multiple target labels. Graded multilabel classification (GMLC) problems go a step further in that they provide a degree of association between an object and each possible label. The goal of a GMLC model is to learn this mapping while minimizing a certain loss function. In this paper, we tackle GMLC problems from a Granular Computing perspective for the first time. The proposed schemes, termed as partitive granular cognitive maps (PGCMs), lean on Fuzzy Cognitive Maps (FCMs) whose input concepts represent cluster prototypes elicited via Fuzzy C-Means whereas the output concepts denote the set of existing labels. We consider three different linkages between the FCM's input and output concepts and learn the causal connections (weight matrix) through a Particle Swarm Optimizer (PSO). During the exploitation phase, the membership grades of a test object to each fuzzy cluster prototype in the PGCM are taken as the initial activation values of the recurrent network. Empirical results on 16 synthetically generated datasets show that the PGCM architecture is capable of accurately solving GMLC instances.

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.

Imbalanced classification deals with learning from data with a disproportional number of samples in its classes. Traditional classifiers exhibit poor behavior when facing this kind of data because they do not take into account the imbalanced class distribution. Four main kinds of solutions exist to solve this problem: modifying the data distribution, modifying the learning algorithm for considering the imbalance representation, including the use of costs for data samples, and ensemble methods. In this paper, we adopt the second type of solution and introduce a classification algorithm for imbalanced data that uses fuzzy rough set theory and ordered weighted average aggregation. The proposal considers different strategies to build a weight vector to take into account data imbalance. Our methods are validated by an extensive experimental study, showing statistically better results than 13 other state-of-the-art methods.

Fuzzy Cognitive Maps (FCM) may be defined as Recurrent Neural Networks that allow causal reasoning. According to the transformation function used for updating the activation value of concepts they can be characterized as discrete or continuous. It is remarkable that FCM having discrete neurons never exhibit chaotic states, but this premise cannot be guaranteed for FCM having continuous concepts. On the other hand, complex Sigmoid FCM resulting from experts or learning algorithms often show chaotic or cyclic patterns, therefore leading to confusing interpretation of the investigated system. The first contribution of this paper is focused on explaining why most studies on FCM stability are not applicable to FCM used on classification or decision-making tasks. Next we describe a non-direct learning methodology based on Swarm Intelligence for improving the system stability once the causal weight estimation is done. The objective here is to find a specific threshold function for each map neuron simulating an external stimulus, instead of using the same transformation function for all concepts. At the end, we can compute more stable maps, so better consistency in hidden patterns is achieved.

In this paper, a review of decision-making models based on the rough set theory is presented. The use of these techniques allows for the presence of uncertainty in computer models that are developed for decision making, and to formulate the decision-making models using the experiences of previous decisions made. Since the formulation of these models differs from the classical approach of decision-making models, in this paper, the models are analyzed and a method is proposed for its implementation.

While Multi-Criteria Decision Making (MCDM) models are focused on selecting the best alternative from a finite number of feasible solutions according to a set of criteria, in Dynamic Multi-Criteria Decision Making (DMCDM) the selection process also takes into account the temporal performance of such alternatives during different time periods. In this paper a new discrete time variable index is proposed, to handling differences in temporal behavior of alternatives, which are not discriminated in preceding dynamic approaches, also considering rating-based perspectives for discrimination of the decision maker by modeling different attitudes to deal with the rating changes along different time periods. Moreover a DMCDM for supplier selection example is provided to illustrate the feasibility and effectiveness of the proposed index.

Many real-world problems have several optima, and the aim of niching optimisation algorithms is to obtain the different global optima, and not only the best solution. One common technique to create niches is the clearing method that removes solutions too close to better ones. Unfortunately, clearing is very sensitive to the niche radius, and its right value depends on the problem (in real-world problems the minimum distance between optima is unknown). In this work we propose a niching algorithm that uses clearing with an adaptive niche radius, that decreases during the run. The proposal uses an external memory that stores current global optima to avoid losing found optima during the clearing process, allowing a non-elitist search. This algorithm applies this clearing method to a mesh of solutions, expanded by the generation of nodes using combination methods between the nodes, their best neighbour, and their nearest current global optima in the population (current global optima are nodes with fitness very similar to current best fitness). The proposal is tested on the competition benchmark proposed in the Special Session Niching Methods for Multimodal Optimization, and compared with other algorithms. The proposal obtains very good results detecting global optima. In comparisons with other algorithm, this proposal obtains the best results, proving to be a very competitive niching algorithm.

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.

Population-based Meta-heuristics are algorithms that can obtain very good results for complex continuous optimisation problems, using the information of a population of solutions. In these algorithms the distribution of solutions is crucial because it has a strong influence of the exploration new regions. In this work, we present a population algorithm, Variable Mesh Optimisation (VMO), in which a set of nodes (potential solutions) is distributed as a mesh. This mesh is initially homogeneously distributed, and then the mesh evolves to a heterogeneous structure resampling the space toward the best neighbours, maintaining at the same time a controlled diversity (avoiding solutions too close to each other). We use a benchmark of multimodal continuous functions to study the influence of the different components of the proposal, and to compare the proposed algorithm with other basic population-based metaheuristics in the literature. The results show that VMO is a very competitive algorithm.

A procedure for the design of new creep resistant ferritic steels that involves a large systematic search of combinations of parameters using a neural network model, was proposed in a paper published few years ago. In the present work we study the effectiveness of the Linguistic Data Summarization technique to be used as a tool to discover a credible and useful creep behavior in a way that it can be used as a guide in the mentioned search. Experiments are performed similar to those discussed in the paper mentioned in order to make an effective comparison of the behavior of the creep. We propose the use of an indicator that measures the degree of representativeness of the linguistic terms for the summarizer in our experiments context. As a result, the effectiveness of the Linguistic Data Summarization to discover hidden creep behavior stored in creep data and the usefulness of the representativeness indicator was confirmed.

In this paper we propose a method to build similarity relations into extended Rough Set Theory. Similarity is estimated using ideas from Granular computing and Case-base reasoning. A new measure is introduced in order to compute the quality of the similarity relation. This work presents a study of a case of a similarity relation based on a global similarity function between two objects, this function includes the weights for each feature and local functions to calculate how the values of a given feature are similar. This approach was proved in the function approximation problem. Promissory results are obtained in several experiments.

In this paper we propose a new model of particle swarm optimization called two-step PSO. The basic idea is to split the heuristic search performed by particles into two stages. We have studied the performance of this new algorithm for the feature selection problem by using the reduct concept of the rough set theory. Experimental results obtained show that the two-step approach improves over the PSO model in calculating reducts, with the same computational cost.

Rough sets theory has opened new trends for the development of the incomplete information theory. Inside this one, the notion of reduct is a very significant one, but to obtain a reduct in a decision system is an expensive computing process although very important in data analysis and knowledge discovery. Because of this, it has been necessary the development of different variants to calculate reducts. The present work look into the utility that offers rough sets model and information theory in feature selection and three methods are presented with the purpose of calculate good reducts. The first algorithm is MRSReduct, a variant of the method RSReduct; both methods consist of a greedy algorithm that uses heuristics to work out good reducts in acceptable times. In this paper we propose other method to find good reducts: RSRed*; this method combines several elements of rough set theory. The new methods are compared with others which are implemented inside pattern recognition, genetic algorithm and ant colony optimization algorithms and the results of the statistical tests are shown.

The accelerated growth of the information volumes on processes, phenomena and reports brings about an increasing interest in the possibility of discovering knowledge from data sets. This is a challenging task because in many cases it deals with extremely large, inherently not structured and fuzzy data, plus the presence of uncertainty. Therefore it is required to know a priori the quality of future procedures without using any additional information. In this paper we propose new measures to evaluate the quality of training sets used by algorithms for learning of supervised classifiers. Our training set assessment relied on measures furnished by rough sets theory. Our experimental results involved three classifiers (k-NN, C-4.5 and MLP) from international data bases. New training sets are built taking into account the results of the measures and the accuracy obtained by the classifiers, with the aim of infer the accuracy that the classifiers would obtain using a new training set. This is possible using a rule generator (C4.5) and a function estimation algorithm (k-NN).

The use of pedagogical methods with the technologies of the information and communications produce a new quality that favors the task of generating, transmitting and sharing knowledge. Such is the case of the pedagogical effect that produces the use of the Concept Maps, which constitute a tool for the management of knowledge, an aid to personalize the learning process, to exchange knowledge, and to learn how to learn. Effective knowledge management maintains the knowledge assets of an organization by identifying and capturing useful information in a usable form, and by supporting refinement and reuse of that information in service of the organization's goals. Concept Mapping provides a framework for making this internal knowledge explicit in a visual form that can easily be examined and shared. However, it does not address how relevant Concept Maps can be retrieved or adapted to new problems. Case-Based Reasoning is playing an increasing role in knowledge retrieval and reuse for corporate memories, and its capabilities are appealing to augment the concept mapping process. In this paper the authors present a new approach to elaborate Intelligent Teaching-Learning Systems, where the techniques of concepts diagrams and Artificial Intelligence are combined, using the Case-Based Reasoning as theoretical framework for the Student Model. The proposed model has been implemented in the computational system HESEI, which has been successfully applied in the teaching-learning process by laymen in the Computer Science field.

In this paper we propose a hybrid approach to feature selection based on Ant Colony System algorithm and Rough Set Theory. Rough Set Theory offers the heuristic function to measure the quality of a single subset. We have studied the influence of the setting of the parameters for this problem, in particular for finding reducts. Experimental results show this hybrid approach is a promising method for features selection.

Rough set theory (RST) is a technique for data analysis. In this paper, we use RST to improve the performance of the k-NN method. The RST is used to edit the training set. We propose two methods to edit training sets, which are based on the lower and upper approximations. Experimental results show a satisfactory performance of the k-NN using these techniques.