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In this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of dG-Choquet integral are both the discrete Choquet integral and the d-Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with dG-Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. © 2021 This work was supported in part by the Spanish Ministry of Science and Technology, under project PID2019-108392GB-I00 (AEI/10.13039/501100011033), by the project PJUPNA-1926 of the Public University of Navarre and by the project VEGA 1/0267/21 .

In Machine Learning an ensemble refers to the combination of several classifiers with the objective of improving the performance of every one of its counterparts. To design an ensemble two main aspects must be considered: how to create a diverse set of classifiers and how to combine their outputs. This work focuses on the latter task. More specifically, we focus on the usage of aggregation functions based on fuzzy measures, such as the Sugeno and Choquet integrals, since they allow to model the coalitions and interactions among the members of the ensemble. In this scenario the challenge is how to construct a fuzzy measure that models the relations among the members of the ensemble. We focus on unsupervised methods for fuzzy measure construction, review existing alternatives and categorize them depending on their features. Furthermore, we intend to address the weaknesses of previous alternatives by proposing a new construction method that obtains the fuzzy measure directly evaluating the performance of each possible subset of classifiers, which can be efficiently computed. To test the usefulness of the proposed fuzzy measure, we focus on the application of ensembles for imbalanced datasets. We consider a set of 66 imbalanced datasets and develop a complete experimental study comparing the reviewed methods and our proposal. This work was supported in part by the Spanish Ministry of Science and Technology (AEI/FEDER, UE) under Project TIN2016-77356-P, and in part by the Public University of Navarra under Project PJUPNA13.

The design of an ensemble of classifiers involves the definition of an aggregation mechanism that produces a single response obtained from the information provided by the classifiers. A specific aggregation methodology that has been studied in the literature is the use of fuzzy integrals, such as the Choquet or the Sugeno integral, where the associated fuzzy measure tries to represent the interaction existing between the classifiers of the ensemble. However, defining the big number of coefficients of a fuzzy measure is not a trivial task and therefore, many different algorithms have been proposed. These can be split into supervised and unsupervised, each class having different learning mechanisms and particularities. Since there is no clear knowledge about the correct method to be used, in this work we propose an experimental study for comparing the performance of eight different learning algorithms under the same framework of imbalanced dataset. Moreover, we also compare the specific fuzzy integral (Choquet or Sugeno) and their synergies with the different fuzzy measure construction methods. This work was partially supported by the Public University of Navarre under the projects PJUPNA13 and PJUPNA1926.

The definition of linguistic terms is a critical part of the construction of any fuzzy classifier. Fuzzy partitioning methods (FPMs) range from simple uniform partitioning to sophisticated optimization algorithms. In this paper we present FUZZ-EQ, a preprocessing algorithm that facilitates the construc-tion of meaningful fuzzy partitions regardless of the FPM used. The proposed approach is radically different from any existing FPM: instead of adjusting the fuzzy sets to the training data, FUZZ-EQ adjusts the training data to a hypothetical uniform partition before applying any FPM. To do so, the original data distribution is transformed into a uniform distribution by applying the probability integral transform. FUZZ-EQ allows FPMs to provide classifiers with more granularity on high density regions, increasing the overall discrimination capability. Additionally, we describe the procedure to reverse this transformation and recover the interpretability of linguistic terms. To assess the effectiveness of our proposal, we conducted an extensive empirical study consisting of 41 classification tasks and 9 fuzzy classifiers with different FPMs, rule induction algorithms, and rule structures. We also tested the scalability of FUZZ-EQ in Big Data classification problems such as HIGGS, with 11 million examples. Experimental results reveal that FUZZ-EQ significantly boosted the classification performance of those classifiers using the same linguistic terms for all rules, including state-of-the-art classifiers such as FARC-HD or IVTURS. This work has been supported by the Spanish Ministry of Science and Technology under the project TIN2016-77356-P and the Public University of Navarre (project PJUPNA13 and predoctoral fellowship).

Trabajo presentado a la 14th International Conference on Hybrid Artificial Intelligence Systems, HAIS 2019. León (España), 2019 It is known that when dealing with interval-valued data, there exist problems associated with the non-existence of a total order. In this work we investigate a reformulation of an interval-valued decomposition strategy for multi-class problems called IVOVO, and we analyze the effectiveness of considering different admissible orders in the aggregation phase of IVOVO. We demonstrate that the choice of an appropriate admissible order allows the method to obtain significant differences in terms of accuracy. This work has been partially supported by the Spanish Ministry of Science and Technology under the project TIN2016-77356-P and the Public University of Navarre under the project PJUPNA13.

Trabajo presentado a la 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2018. Cádiz, 11-15 de junio de 2018 In this work we study the usage of different families of fusion functions for combining classifiers in a multiple classifier system of One-vs-One (OVO) classifiers. OVO is a decomposition strategy used to deal with multi-class classification problems, where the original multi-class problem is divided into as many problems as pair of classes. In a multiple classifier system, classifiers coming from different paradigms such as support vector machines, rule induction algorithms or decision trees are combined. In the literature, several works have addressed the usage of classifier selection methods for these kinds of systems, where the best classifier for each pair of classes is selected. In this work, we look at the problem from a different perspective aiming at analyzing the behavior of different families of fusion functions to combine the classifiers. In fact, a multiple classifier system of OVO classifiers can be seen as a multi-expert decision making problem. In this context, for the fusion functions depending on weights or fuzzy measures, we propose to obtain these parameters from data. Backed-up by a thorough experimental analysis we show that the fusion function to be considered is a key factor in the system. Moreover, those based on weights or fuzzy measures can allow one to better model the aggregation problem. This work was supported in part by the Spanish Ministry of Science and Technology under Project TIN2016-77356-P (AEI/FEDER, UE).