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.

The increasing adoption of artificial intelligence (AI) in critical domains such as healthcare, law, and defense demands robust mechanisms to ensure transparency and explainability in decision‐making processes. While machine learning and deep learning algorithms have advanced significantly, their growing complexity presents persistent interpretability challenges. Existing maturity frameworks, such as Capability Maturity Model Integration, fall short in addressing the distinct requirements of explainability in AI systems, particularly where ethical compliance and public trust are paramount. To address this gap, we propose the Maturity Model for eXplainable Artificial Intelligence: Analysis and Evaluation (MM4XAI‐AE), a domain‐agnostic maturity model tailored to assess and guide the practical deployment of explainability in AI‐based applications. The model integrates two complementary components: an analysis model and an evaluation model, structured across four maturity levels—operational, justified, formalized, and managed. It evaluates explainability across three critical dimensions: technical foundations, structured design, and human‐centered explainability. MM4XAI‐AE is grounded in the PAG‐XAI framework, emphasizing the interrelated dimensions of practicality, auditability, and governance, thereby aligning with current reflections on responsible and trustworthy AI. The MM4XAI‐AE model is empirically validated through a structured evaluation of thirteen published AI applications from diverse sectors, analyzing their design and deployment practices. The results show a wide distribution across maturity levels, underscoring the model’s capacity to identify strengths, gaps, and actionable pathways for improving explainability. This work offers a structured and scalable framework to standardize explainability practices and supports researchers, developers, and policymakers in fostering more transparent, ethical, and trustworthy AI systems.

Anomaly detection is the process of identifying observations that differ greatly from the majority of data. Unsupervised anomaly detection aims to find outliers in data that is not labeled, therefore, the anomalous instances are unknown. The exponential data generation has led to the era of Big Data. This scenario brings new challenges to classic anomaly detection problems due to the massive and unsupervised accumulation of data. Traditional methods are not able to cop up with computing and time requirements of Big Data problems. In this paper, we propose four distributed algorithm designs for Big Data anomaly detection problems: HBOS_BD, LODA_BD, LSCP_BD, and XGBOD_BD. They have been designed following the MapReduce distributed methodology in order to be capable of handling Big Data problems. These algorithms have been integrated into an Spark Package, focused on static and dynamic Big Data anomaly detection tasks, namely AnomalyDSD. Experiments using a real-world case of study have shown the performance and validity of the proposals for Big Data problems. With this proposal, we have enabled the practitioner to efficiently and effectively detect anomalies in Big Data datasets, where the early detection of an anomaly can lead to a proper and timely decision.

Deep learning models like chatGPT exemplify AI success but necessitate a deeper understanding of trust in critical sectors. Trust can be achieved using counterfactual explanations, which is how humans become familiar with unknown processes; by understanding the hypothetical input circumstances under which the output changes. We argue that the generation of counterfactual explanations requires several aspects of the generated counterfactual instances, not just their counterfactual ability. We present a framework for generating counterfactual explanations that formulate its goal as a multiobjective optimization problem balancing three objectives: plausibility; the intensity of changes; and adversarial power. We use a generative adversarial network to model the distribution of the input, along with a multiobjective counterfactual discovery solver balancing these objectives. We demonstrate the usefulness of six classification tasks with image and 3D data confirming with evidence the existence of a trade-off between the objectives, the consistency of the produced counterfactual explanations with human knowledge, and the capability of the framework to unveil the existence of concept-based biases and misrepresented attributes in the input domain of the audited model. Our pioneering effort shall inspire further work on the generation of plausible counterfactual explanations in real-world scenarios where attribute-/concept-based annotations are available for the domain under analysis.

Explainable artificial intelligence is proposed to provide explanations for reasoning performed by artificial intelligence. There is no consensus on how to evaluate the quality of these explanations, since even the definition of explanation itself is not clear in the literature. In particular, for the widely known local linear explanations, there are qualitative proposals for the evaluation of explanations, although they suffer from theoretical inconsistencies. The case of image is even more problematic, where a visual explanation seems to explain a decision while detecting edges is what it really does. There are a large number of metrics in the literature specialized in quantitatively measuring different qualitative aspects, so we should be able to develop metrics capable of measuring in a robust and correct way the desirable aspects of the explanations. Some previous papers have attempted to develop new measures for this purpose. However, these measures suffer from lack of objectivity or lack of mathematical consistency, such as saturation or lack of smoothness. In this paper, we propose a procedure called REVEL to evaluate different aspects concerning the quality of explanations with a theoretically coherent development which do not have the problems of the previous measures. This procedure has several advances in the state of the art: it standardizes the concepts of explanation and develops a series of metrics not only to be able to compare between them but also to obtain absolute information regarding the explanation itself. The experiments have been carried out on four image datasets as benchmark where we show REVEL’s descriptive and analytical power.

Ordinal regression addresses the problem of predicting non-numerical ordered classes. It walks a fine line between standard regression and classification, and the problem is often addressed from one of these perspectives. This can lead to suboptimal results as the ordinal information in the data may not be properly exploited. In this work we propose a distance metric learning algorithm to handle ordinal regression. Our model aims at optimizing the number of ordered sequences in local neighborhoods of the data, so that the learned distance can then be used by a distance-based predictor and improve its performance in ordinal regression problems. We evaluate our algorithm on several ordinal regression datasets and show that it outperforms the current distance metric learning for ordinal regression proposals, as well as being competitive with respect to the state-of-the-art of ordinal regression. The current paper is an extended abstract for the work [1].

Urban resettlement projects involve a large number of stakeholders and impose tremendous cost. Developing resettlement plans and reaching an agreement amongst stakeholders about resettlement plans at a reasonable cost are some of the key issues in urban resettlement. From this perspective, urban resettlement is a typical large-scale group decision-making (GDM) problem, which is challenging because of the scale of participants and the requirement of high consensus levels. Observing that residents who are affected by a resettlement project often have tight social connections, this study proposes a framework to improve the consensus reaching and uses the minimum consensus cost to reduce the total cost for urban resettlement projects with more than 1000 participants. Firstly, we construct a network topology that consists of two layers to deal with incomplete social relationships amongst large-scale participants. An inner layer consists of participants whose preference similarities and trust relations are known. Meanwhile, an outside layer includes participants whose trust relations cannot be determined. Secondly, we develop a classification method to classify participants into small subgroups based on their preference similarities. We can then connect the participants whose trust relations are unknown (the outside layer) with the ones in the inner layer using the classification results. To facilitate effective consensus reaching in large-scale social network GDM, we develop a three-step approach to reconcile conflicting preferences and accelerate the consensus process at the minimum cost. A real-life urban resettlement example is used to validate the proposed approach. Results show that the proposed approach can reduce the total consensus cost compared with the other two practices used in the actual urban resettlement operations.

Data in the real world is far from being perfect. The appearance of noise is a common issue that arises from the limitations of data acquisition mechanisms and human knowledge. In classification, label noise will hinder the performance of almost all classifiers, inducing a bias in the built model. While label noise has recently attracted researchers’ attention in standard classification, it has only recently begun to be studied in multiple instance classification. In this work, we propose the usage of filtering algorithms for multiple instance classification that are able to reduce the impact of negative instances within the bags. In order to do so, we decompose the bags to form a standard classification problem that can be efficiently treated by a specialized noise filter. Such a decomposition is tackled in different ways, with the aim of exploiting the knowledge offered by the examples from opposite bags. The bags are then rebuilt, without the identified noise instances. In our experiments, we show that by applying our approach we can diminish the impact of noise and even obtain better results at 0% noise level for several classifiers. Our approach sets out a promising approach to dealing with noise in the bags of multiple instance datasets and further improve the classification rate of the built models.

Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data. However, some properties can cause datasets to be problematic to classify. In order to evaluate a dataset a priori, data complexity metrics have been used extensively. They provide information regarding different intrinsic characteristics of the data, which serve to evaluate classifier compatibility and a course of action that improves performance. However, most complexity metrics focus on just one characteristic of the data, which can be insufficient to properly evaluate the dataset towards the classifiers' performance. In fact, class overlap, a very detrimental feature for the classification process (especially when imbalance among class labels is also present) is hard to assess. This research work focuses on revisiting complexity metrics based on data morphology. In accordance to their nature, the premise is that they provide both good estimates for class overlap, and great correlations with the classification performance. For that purpose, a novel family of metrics have been developed. Being based on ball coverage by classes, they are named after Overlap Number of Balls. Finally, some prospects for the adaptation of the former family of metrics to singular (more complex) problems are discussed.

Understanding consumer behaviors and how consumers react to marketing campaigns and viral word-of-mouth processes is crucial for marketers. Classical approaches try to infer this information from a global top-down perspective. However, a more suitable and natural approach is to model consumer behaviors in a heterogeneous and decentralized bottom-up approach. In this case, each virtual consumer has her own mental state and decision-making strategies to simulate her purchase decisions. The system of virtual consumers generates the global sales and a marketer can understand the rules that govern the market. A well-known paradigm to model these systems is agent-based modeling (ABM). In this manuscript we present an ABM where the brand preferences of the consumer agents are modeled using 2-tuple fuzzy linguistic variables. These variables represent the perceptions these consumers have on the different aspects or drivers every product available in the market has (e.g., price or quality). The product selection process of the agents is based on those perceptions and a utility maximization rule. This rule requires a fuzzy aggregation of the fuzzy linguistic perceptions about the products. Our proposal employs an ordered weighted average (OWA) to aggregate them. Our experiments show this approach does not suffer any loss of information when applied on data from real markets. Hence it is a suitable representation of the products preferences, normally represented by qualitative values in marketing surveys. To the best of our knowledge, this is the first work integrating a marketing ABM with fuzzy linguistic modeling.

The social network group decision-making is popular due to the advantages of social relationships in the consensus reaching process, especially the trust relationships. To explore the effects of trust on consensus, some minimum cost consensus models are proposed based on implicit trust between individuals and the moderator. The implicit trust is computed based on the similarity of opinions and it is implied into the traditional minimum cost consensus model to obtain a new quadratic programming problem and the related dual problem. The weights of individuals can be determined based on implicit trust and can be used to modify the possible deviations among individuals’ adjustment costs. A numerical example and the comparative analysis are given to analyze the effectiveness of the proposed models, which suggests that individuals are willing to give up some benefit to reach consensus due to their implicit trust to the moderator and make minor revisions to their adjustment costs due to their implicit trust to each other.

The quality of the data is directly related to the quality of the models drawn from that data. For that reason, many research is devoted to improve the quality of the data and to amend errors that it may contain. One of the most common problems is the presence of noise in classification tasks, where noise refers to the incorrect labeling of training instances. This problem is very disruptive, as it changes the decision boundaries of the problem. Big Data problems pose a new challenge in terms of quality data due to the massive and unsupervised accumulation of data. This Big Data scenario also brings new problems to classic data preprocessing algorithms, as they are not prepared for working with such amounts of data, and these algorithms are key to move from Big to Smart Data. In this paper, an iterative ensemble filter for removing noisy instances in Big Data scenarios is proposed. Experiments carried out in six Big Data datasets have shown that our noise filter outperforms the current state-of-the-art noise filter in Big Data domains. It has also proved to be an effective solution for transforming raw Big Data into Smart Data.

The current evolution in multidisciplinary learning analytics research poses significant challenges for the exploitation of behavior analysis by fusing data streams toward advanced decision-making. The identification of students that are at risk of withdrawals in higher education is connected to numerous educational policies, to enhance their competencies and skills through timely interventions by academia. Predicting student performance is a vital decision-making problem including data from various environment modules that can be fused into a homogenous vector to ascertain decision-making. This research study exploits a temporal sequential classification problem to predict early withdrawal of students, by tapping the power of actionable smart data in the form of students' interactional activities with the online educational system, using the freely available Open University Learning Analytics data set by employing deep long short-term memory (LSTM) model. The deployed LSTM model outperforms baseline logistic regression and artificial neural networks by 10.31% and 6.48% respectively with 97.25% learning accuracy, 92.79% precision, and 85.92% recall.

Preference relations have been widely used in group decision-making (GDM) problems. Recently, a new kind of preference relations called fuzzy preference relations with self-confidence (FPRs-SC) has been introduced, which allow experts to express multiple self-confidence levels when providing their preferences. This paper focuses on the analysis of additive consistency for FPRs-SC and its application in GDM problems. To do that, some operational laws for FPRs-SC are proposed. Subsequently, an additive consistency index that considers both the fuzzy preference values and self-confidence is presented to measure the consistency level of an FPR-SC. Moreover, an iterative algorithm that adjusts both the fuzzy preference values and self-confidence levels is proposed to repair the inconsistency of FPRs-SC. When an acceptable additive consistency level for FPRs-SC is achieved, the collective FPR-SC can be computed. We aggregate the individual FPRs-SC using a self-confidence indices-based induced ordered weighted averaging operator. The inherent rule for aggregation is to give more importance to the most self-confident experts. In addition, a self-confidence score function for FPRs-SC is designed to obtain the best alternative in GDM with FPRs-SC. Finally, the feasibility and validity of the research are demonstrated with an illustrative example and some comparative analyses.

Fingerprint classification is one of the most common approaches to accelerate the identification in large databases of fingerprints. Fingerprints are grouped into disjoint classes, so that an input fingerprint is compared only with those belonging to the predicted class, reducing the penetration rate of the search. The classification procedure usually starts by the extraction of features from the fingerprint image, frequently based on visual characteristics. In this work, we propose an approach to fingerprint classification using convolutional neural networks, which avoid the necessity of an explicit feature extraction process by incorporating the image processing within the training of the classifier. Furthermore, such an approach is able to predict a class even for low-quality fingerprints that are rejected by commonly used algorithms, such as FingerCode. The study gives special importance to the robustness of the classification for different impressions of the same fingerprint, aiming to minimize the penetration in the database. In our experiments, convolutional neural networks yielded better accuracy and penetration rate than state-of-the-art classifiers based on explicit feature extraction. The tested networks also improved on the runtime, as a result of the joint optimization of both feature extraction and classification.

With the advent of large-scale problems, feature selection has become a fundamental preprocessing step to reduce input dimensionality. The minimum-redundancy-maximum-relevance (mRMR) selector is considered one of the most relevant methods for dimensionality reduction due to its high accuracy. However, it is a computationally expensive technique, sharply affected by the number of features. This paper presents fast-mRMR, an extension of mRMR, which tries to overcome this computational burden. Associated with fast-mRMR, we include a package with three implementations of this algorithm in several platforms, namely, CPU for sequential execution, GPU (graphics processing units) for parallel computing, and Apache Spark for distributed computing using big data technologies.

Imbalanced classification is one of the most challenging machine learning problem. Recent studies show, that often the uneven ratio of objects in classes is not the biggest factor, determining the drop of classification accuracy. It is also related to some difficulties embedded in the nature of the data. In this paper we study the different types of minority class examples and distinguish four groups of objects - safe, borderline, rare and outliers. To deal with the imbalance problem, we use a one-class classification, that is focused on a proper identification of the minority class samples. We further augment this model by incorporating the knowledge about the minority object types in the training dataset. This is done applying weighted one-class classifier and adjusting weights assigned to minority class objects, depending on their type. A strategy for calculating the new weights for minority examples is proposed. Experimental analysis, carried on a set of benchmark datasets, confirms that the proposed model can achieve a satisfactory recognition rate and often outperform other state-of-the-art methods, dedicated to the imbalanced classification.

The necessity of dealing with uncertainty in real world problems has been a long-term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type-2 fuzzy sets, interval-valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so-called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.

Bibliometric mapping and visualization techniques represent one of the main pillars in the field of scientometrics. Traditionally, the main methodologies employed for representing data are multidimensional scaling, principal component analysis, or correspondence analysis. In this paper we aim to present a visualization methodology known as biplot analysis for representing bibliometric and science and technology indicators. A biplot is a graphical representation of multivariate data, where the elements of a data matrix are represented according to dots and vectors associated with the rows and columns of the matrix. In this paper, we explore the possibilities of applying biplot analysis in the research policy area. More specifically, we first describe and introduce the reader to this methodology and secondly, we analyze its strengths and weaknesses through 3 different case studies: countries, universities, and scientific fields. For this, we use a biplot analysis known as JK ‐biplot. Finally, we compare the biplot representation with other multivariate analysis techniques. We conclude that biplot analysis could be a useful technique in scientometrics when studying multivariate data, as well as an easy‐to‐read tool for research decision makers.

Discretization is an essential preprocessing technique used in many knowledge discovery and data mining tasks. Its main goal is to transform a set of continuous attributes into discrete ones, by associating categorical values to intervals and thus transforming quantitative data into qualitative data. In this manner, symbolic data mining algorithms can be applied over continuous data and the representation of information is simplified, making it more concise and specific. The literature provides numerous proposals of discretization and some attempts to categorize them into a taxonomy can be found. However, in previous papers, there is a lack of consensus in the definition of the properties and no formal categorization has been established yet, which may be confusing for practitioners. Furthermore, only a small set of discretizers have been widely considered, while many other methods have gone unnoticed. With the intention of alleviating these problems, this paper provides a survey of discretization methods proposed in the literature from a theoretical and empirical perspective. From the theoretical perspective, we develop a taxonomy based on the main properties pointed out in previous research, unifying the notation and including all the known methods up to date. Empirically, we conduct an experimental study in supervised classification involving the most representative and newest discretizers, different types of classifiers, and a large number of data sets. The results of their performances measured in terms of accuracy, number of intervals, and inconsistency have been verified by means of nonparametric statistical tests. Additionally, a set of discretizers are highlighted as the best performing ones.

This article presents a new open‐source software tool, SciMAT , which performs science mapping analysis within a longitudinal framework. It provides different modules that help the analyst to carry out all the steps of the science mapping workflow. In addition, SciMAT presents three key features that are remarkable in respect to other science mapping software tools: (a) a powerful preprocessing module to clean the raw bibliographical data, (b) the use of bibliometric measures to study the impact of each studied element, and (c) a wizard to configure the analysis.

Science mapping aims to build bibliometric maps that describe how specific disciplines, scientific domains, or research fields are conceptually, intellectually, and socially structured. Different techniques and software tools have been proposed to carry out science mapping analysis. The aim of this article is to review, analyze, and compare some of these software tools, taking into account aspects such as the bibliometric techniques available and the different kinds of analysis.

Abstract Thomson Reuters' Web of Science (WoS) is undoubtedly a great tool for scientiometrics purposes. It allows one to retrieve and compute different measures such as the total number of papers that satisfy a particular condition; however, it also is well known that this tool imposes several different restrictions that make obtaining certain results difficult. One of those constraints is that the tool does not offer the total count of documents in a dataset if it is larger than 100,000 items. In this article, we propose and analyze different approaches that involve partitioning the search space (using the Source field) to retrieve item counts for very large datasets from the WoS. The proposed techniques improve previous approaches: They do not need any extra information about the retrieved dataset (thus allowing completely automatic procedures to retrieve the results), they are designed to avoid many of the restrictions imposed by the WoS, and they can be easily applied to almost any query. Finally, a description of WoS Query Partitioner, a freely available and online interactive tool that implements those techniques, is presented.

The aim of this paper is to propose a procedure to estimate missing preference values when dealing with incomplete fuzzy linguistic preference relations assessed using a two-tuple fuzzy linguistic approach. This procedure attempts to estimate the missing information in an individual incomplete fuzzy linguistic preference relation using only the preference values provided by the respective expert. It is guided by the additive consistency property to maintain experts' consistency levels. Additionally, we present a selection process of alternatives in group decision making with incomplete fuzzy linguistic preference relations and analyze the use of our estimation procedure in the decision process. © 2008 Wiley Periodicals, Inc.

Most real-coded genetic algorithm research has focused on developing effective crossover operators, and as a result, many different types of crossover operators have been proposed. Some forms of crossover operators are more suitable to tackle certain problems than others, even at the different stages of the genetic process in the same problem. For this reason, techniques that combine multiple crossovers, called hybrid crossover operators, have been suggested as alternative schemes to the common practice of applying only one crossover model to all the elements in the population. On the other hand, there are operators with multiple offsprings, more than two descendants from two parents, which present a better behavior than the operators with only two descendants, and achieve a good balance between exploration and exploitation. © 2009 Wiley Periodicals, Inc.

Abstract In this article, our interest is focused on the automatic learning of Boolean queries in information retrieval systems (IRSs) by means of multi‐objective evolutionary algorithms considering the classic performance criteria, precision and recall. We present a comparative study of four well‐known, general‐purpose, multi‐objective evolutionary algorithms to learn Boolean queries in IRSs. These evolutionary algorithms are the Nondominated Sorting Genetic Algorithm (NSGA‐II), the first version of the Strength Pareto Evolutionary Algorithm (SPEA), the second version of SPEA (SPEA2), and the Multi‐Objective Genetic Algorithm (MOGA).

In this paper, we present a procedure to estimate missing preference values when dealing with pairwise comparison and heterogeneous information. This procedure attempts to estimate the missing information in an expert's incomplete preference relation using only the preference values provided by that particular expert. Our procedure to estimate missing values can be applied to incomplete fuzzy, multiplicative, interval-valued, and linguistic preference relations. Clearly, it would be desirable to maintain experts' consistency levels. We make use of the additive consistency property to measure the level of consistency and to guide the procedure in the estimation of the missing values. Finally, conditions that guarantee the success of our procedure in the estimation of all the missing values of an incomplete preference relation are given. © 2008 Wiley Periodicals, Inc.

Crossover operators with multiple descendents produce more than two offspring for each pair of parents. They were suggested as an alternative method to the common practice of generating only two offspring per couple. An offspring selection mechanism is responsible for choosing the two offspring that become the children contributed by the mating. Recently, there has been an increasing interest in incorporating this crossover scheme into real-coded genetic algorithm models because its operation was particularly suitable to attain reliable and accurate solutions for many continuous optimization problems. In this paper, we undertake an extensive empirical study of the main factors that affect the performance of real-parameter crossover operator with multiple descendents. To do this, we focus our attention on three well-known neighborhood-based real-parameter crossover operators, BLX-α, fuzzy recombination, and PNX. The experimental results obtained confirm that the generation of multiple descendents along with the offspring selection mechanism that chooses the two best offspring may enhance the operation of these three crossover operators. Another important finding from our experiments is that real-coded genetic algorithms with crossover operators with multiple descendents are more efficient than standard real-coded genetic algorithms, that is, they offer solutions with higher quality, requiring fewer fitness function evaluations. © 2008 Wiley Periodicals, Inc.

This article presents a study on the use of parametrized operators in the Inference System of linguistic fuzzy systems adapted by evolutionary algorithms, for achieving better cooperation among fuzzy rules. This approach produces a kind of rule cooperation by means of the inference system, increasing the accuracy of the fuzzy system without losing its interpretability. We study the different alternatives for introducing parameters in the Inference System and analyze their interpretation and how they affect the rest of the components of the fuzzy system. We take into account three applications in order to analyze their accuracy in practice. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1035–1064, 2007.

This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics-based Takagi–Sugeno–Kang (TSK) rules. This allow us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy nature of the TSK rules. To do so, a two-stage evolutionary algorithm based on MOGUL (a methodology to obtain Genetic Fuzzy Rule-Based Systems under the Iterative Rule Learning approach) has been developed to consider the interaction between input and output variables. The first stage performs a local identification of prototypes to obtain a set of initial local semantics-based TSK rules, following the Iterative Rule Learning approach and based on an evolutionary generation process within MOGUL (taking as a base some initial linguistic fuzzy partitions). Because this generation method induces competition among the fuzzy rules, a postprocessing stage to improve the global system performance is needed. Two different processes are considered at this stage, a genetic niching-based selection process to remove redundant rules and a genetic tuning process to refine the fuzzy model parameters. The proposal has been tested with two real-world problems, achieving good results. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 909–941, 2007.

Before implementing a design of a large engineering system different design proposals are evaluated. The information used by experts to evaluate different options may be vague and/or incomplete. Although different probabilistic tools and techniques have been used to deal with these kinds of problems, it seems better to use the fuzzy linguistic approach to model vagueness and the Dempster-Shafter theory of evidence for modeling incompleteness and ignorance. In the evaluation of alternative designs, different criteria can be considered. In this article an evaluation process is developed in terms of Safety and Cost analysis. Both criteria involve uncertainty, vagueness, and ignorance due to their nature. Therefore, we propose an evaluation process defined in a linguistic framework where both criteria will be conducted in different utility spaces, i.e., in a multigranular linguistic domain. Once the evaluation framework has been defined, we present an evaluation process based on a Multi-Expert Multi-Criteria decision model that will be able to deal with multigranular linguistic information without loss of information in order to evaluate different design options for an engineering system in a precise manner. Accordingly, we propose the use of a multigranular linguistic model based on the Linguistic Hierarchies presented by Herrera and Martínez (“A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multi-expert decision-making.” IEEE Trans Syst Man Cybern B 2001;31(2):227–234). © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1161–1194, 2005.

In this article, we introduce the induced ordered weighted geometric (IOWG) operator and its properties. This is a more general type of OWG operator, which is based on the induced ordered weighted averaging (IOWA) operator. We provide some IOWG operators to aggregate multiplicative preference relations in group decision-making (GDM) problems. In particular, we present the importance IOWG (I-IOWG) operator, which induces the ordering of the argument values based on the importance of the information sources; the consistency IOWG (C-IOWG) operator, which induces the ordering of the argument values based on the consistency of the information sources; and the preference IOWG (P-IOWG) operator, which induces the ordering of the argument values based on the relative preference values associated with each one of them. We also provide a procedure to deal with “ties” regarding the ordering induced by the application of one of these IOWG operators. This procedure consists of a sequential application of the aforementioned IOWG operators. Finally, we analyze the reciprocity and consistency properties of the collective multiplicative preference relations obtained using IOWG operators. © 2004 Wiley Periodicals, Inc.

This special issue encompasses eight papers devoted to recent developments in the field of preference modeling.The issue originates from presentations at the EUROFUSE Workshop on Preference Modeling and Applications (EUROFUSE 2001) that was held in Granada, Spain, April 25-27, 2001.These eight original contributions have been revised thoroughly and expanded to become the articles currently presented in this issue.Preference modeling is a fundamental step in solving problems in various fields such as economics, medical diagnosis, information retrieval, decision theory, etc.Most of these problems take place in a complex environment where uncertain and imprecise knowledge and possibly vague preferences have to be considered.To face such complexity, preference modeling requires the use of specific techniques and concepts that allow the available information to be represented appropriately.As is well known, the fuzzy approach has led to considerable advances in preference modeling, mainly because the use of fuzzy techniques increases the reliability and flexibility of decision models.The present issue includes different proposals of fuzzy preference modeling in several application fields.The first group of articles is focused on the study of different aspects of preference modeling in Multicriteria Decision Making

The ordered weighted geometric (OWG) operator is an aggregation operator that is based on the ordered weighted averaging (OWA) operator and the geometric mean. Its application in multicriteria decision making (MCDM) under multiplicative preference relations has been presented. Some families of OWG operators have been defined. In this article, we present the origin of the OWG operator and we review its relationship to the OWA operator in MCDM models. We show a study of its use in multiplicative decision-making models by providing the conditions under which reciprocity and consistency properties are maintained in the aggregation of multiplicative preference relations performed in the selection process. © 2003 Wiley Periodicals, Inc.

The main real-coded genetic algorithm (RCGA) research effort has been spent on developing efficient crossover operators. This study presents a taxonomy for this operator that groups its instances in different categories according to the way they generate the genes of the offspring from the genes of the parents. The empirical study of representative crossovers of all the categories reveals concrete features that allow the crossover operator to have a positive influence on RCGA performance. They may be useful to design more effective crossover models. © 2003 Wiley Periodicals, Inc.

The main aim of this paper is to present MOGUL, a Methodology to Obtain Genetic fuzzy rule-based systems Under the iterative rule Learning approach. MOGUL will consist of some design guidelines that allow us to obtain different genetic fuzzy rule-based systems, i.e., evolutionary algorithm-based processes to automatically design fuzzy rule-based systems by learning and/or tuning the fuzzy rule base, following the same generic structure and able to cope with problems of a different nature. A specific evolutionary learning process obtained from the paradigm proposed to design unconstrained approximate Mamdani-type fuzzy rule-based systems will be introduced, and its accuracy in the solving of a real-world electrical engineering problem will be analyzed. ©1999 John Wiley & Sons, Inc.

Genetic algorithm behavior is determined by the exploration/exploitation balance kept throughout the run. When this balance is disproportionate, the premature convergence problem will probably appear, causing a drop in the genetic algorithm's efficacy. One approach presented for dealing with this problem is the distributed genetic algorithm model. Its basic idea is to keep, in parallel, several subpopulations that are processed by genetic algorithms, with each one being independent from the others. Furthermore, a migration operator produces a chromosome exchange between the subpopulations. Making distinctions between the subpopulations of a distributed genetic algorithm by applying genetic algorithms with different configurations, we obtain the so-called heterogeneous distributed genetic algorithms. In this paper, we present a hierarchical model of distributed genetic algorithms in which a higher level distributed genetic algorithm joins different simple distributed genetic algorithms. Furthermore, with the union of the hierarchical structure presented and the idea of the heterogeneous distributed genetic algorithms, we propose a type of heterogeneous hierarchical distributed genetic algorithms, the hierarchical gradual distributed genetic algorithms. Experimental results show that the proposals consistently outperform equivalent sequential genetic algorithms and simple distributed genetic algorithms. ©1999 John Wiley & Sons, Inc.

In this paper, we present a multistage genetic learning process for obtaining linguistic fuzzy rule-based classification systems that integrates fuzzy reasoning methods cooperating with the fuzzy rule base and learns the best set of linguistic hedges for the linguistic variable terms. We show the application of the genetic learning process to two well known sample bases, and compare the results with those obtained from different learning algorithms. The results show the good behavior of the proposed method, which maintains the linguistic description of the fuzzy rules. © 1998 John Wiley & Sons, Inc.

Genetic algorithms are adaptive methods which may be used as approximation heuristic for search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover, and mutation. A great problem in the use of genetic algorithms is the premature convergence, a premature stagnation of the search caused by the lack of diversity in the population and a disproportionate relationship between exploitation and exploration. The crossover operator is considered one of the most determinant elements for solving this problem. In this article we present two types of crossover operators based on fuzzy connectives for real-coded genetic algorithms. The first type is designed to keep a suitable sequence between the exploration and the exploitation along the genetic algorithm's run, the dynamic fuzzy connectives-based crossover operators, the second, for generating offspring near to the best parents in order to offer diversity or convergence in a profitable way, the heuristic fuzzy connectives-based crossover operators. We combine both crossover operators for designing dynamic heuristic fuzzy connectives-based crossover operators that show a robust behavior. © 1996 John Wiley & Sons, Inc.

This article discusses the applications of fuzzy boolean programming problems for representing and reasoning with propositional knowledge. the use of the models provided by the fuzzy boolean problems are proposed to answer imprecise questions in precisely stated knowledge-based systems. Also, the advantages of using fuzzy boolean programming instead of classical ones are presented in the framework of propositional knowledge. © 1994 John Wiley & Sons, Inc.