# Person: Pereira Dimuro, Graçaliz

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Pereira Dimuro

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Graçaliz

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Automática y Computación

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0000-0001-6986-9888

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811336

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Publication Open Access Aggregation functions based on the Choquet integral applied to image resizing(Atlantis Press, 2019) Bueno, Jéssica C. S.; Dias, Camila A.; Pereira Dimuro, Graçaliz; Santos, Helida; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasShow more The rising volume of data and its high complexity has brought the need of developing increasingly efficient knowledge extraction techniques, which demands efficiency both in computational cost and in accuracy. Most of problems that are handled by these techniques has complex information to be identified. So, machine learning methods are frequently used, where a variety of functions can be applied in the different steps that are employed in their architecture. One of them is the use of aggregation functions aiming at resizing images. In this context, we introduce a study of aggregation functions based on the Choquet integral, whose main characteristic in comparison with other aggregation functions is that it considers, through fuzzy measure, the interaction between the elements to be aggregated. Thus, our main goal is to present an evaluation study of the performance of the standard Choquet integral the and copula-based generalization of the Choquet integral in relation to the maximum and mean functions, looking for results that may be better than the aggregation functions commonly applied. The results of such comparisons are promising, when evaluated through image quality metrics.Show more Publication Open Access VCI-LSTM: Vector choquet integral-based long short-term memory(IEEE, 2022) Ferrero Jaurrieta, Mikel; Takáč, Zdenko; Fernández Fernández, Francisco Javier; Horanská, Lubomíra; Pereira Dimuro, Graçaliz; Montes, Susana; Díaz, Irene; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Choquet integral is a widely used aggregation operator on one-dimensional and interval-valued information, since it is able to take into account the possible interaction among data. However, there are many cases where the information taken into account is vectorial, such as Long Short-Term Memories (LSTM). LSTM units are a kind of Recurrent Neural Networks that have become one of the most powerful tools to deal with sequential information since they have the power of controlling the information flow. In this paper, we first generalize the standard Choquet integral to admit an input composed by $n$-dimensional vectors, which produces an $n$-dimensional vector output. We study several properties and construction methods of vector Choquet integrals. Then, we use this integral in the place of the summation operator, introducing in this way the new VCI-LSTM architecture. Finally, we use the proposed VCI-LSTM to deal with two problems: sequential image classification and text classification.Show more Publication Open Access Enhancing LSTM for sequential image classification by modifying data aggregation(IEEE, 2021) Takáč, Zdenko; Ferrero Jaurrieta, Mikel; Horanská, Lubomíra; Krivonakova, Nada; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Recurrent Neural Networks (RNN) model sequential information and are commonly used for the analysis of time series. The most usual operation to fuse information in RNNs is the sum. In this work, we use a RNN extended type, Long Short-Term Memory (LSTM) and we use it for image classification, to which we give a sequential interpretation. Since the data used may not be independent to each other, we modify the sum operator of an LSTM unit using the n-dimensional Choquet integral, which considers possible data coalitions. We compare our methods to those based on usual aggregation functions, using the datasets Fashion-MNIST and MNIST.Show more Publication Open Access A proposal for tuning the α parameter in CαC-integrals for application in fuzzy rule-based classification systems(Springer, 2020) Lucca, Giancarlo; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Callejas Bedregal, Benjamin; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasShow more In this paper, we consider the concept of extended Choquet integral generalized by a copula, called CC-integral. In particular, we adopt a CC-integral that uses a copula defined by a parameter α, which behavior was tested in a previous work using different fixed values. In this contribution, we propose an extension of this method by learning the best value for the parameter α using a genetic algorithm. This new proposal is applied in the fuzzy reasoning method of fuzzy rule-based classification systems in such a way that, for each class, the most suitable value of the parameter α is obtained, which can lead to an improvement on the system's performance. In the experimental study, we test the performance of 4 different so called CαC-integrals, comparing the results obtained when using fixed values for the parameter α against the results provided by our new evolutionary approach. From the obtained results, it is possible to conclude that the genetic learning of the parameter α is statistically superior than the fixed one for two copulas. Moreover, in general, the accuracy achieved in test is superior than that of the fixed approach in all functions. We also compare the quality of this approach with related approaches, showing that the methodology proposed in this work provides competitive results. Therefore, we demonstrate that CαC-integrals with α learned genetically can be considered as a good alternative to be used in fuzzy rule-based classification systems.Show more Publication Open Access d-Choquet integrals: Choquet integrals based on dissimilarities(Elsevier, 2020) Bustince Sola, Humberto; Mesiar, Radko; Fernández Fernández, Francisco Javier; Galar Idoate, Mikel; Paternain Dallo, Daniel; Altalhi, A. H.; Pereira Dimuro, Graçaliz; Callejas Bedregal, Benjamin; Takáč, Zdenko; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13Show more The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These functions are a generalization of the 'standard' Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the class of all 'standard' Choquet integrals but the use of dissimilarities provides higher flexibility and generality. We show that some d-Choquet integrals are aggregation/pre-aggregation/averaging/functions and some of them are not. The conditions under which this happens are stated and other properties of the d-Choquet integrals are studied.Show more Publication Open Access Neuro-inspired edge feature fusion using Choquet integrals(Elsevier, 2021) Marco Detchart, Cedric; Lucca, Giancarlo; López Molina, Carlos; Miguel Turullols, Laura de; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more It is known that the human visual system performs a hierarchical information process in which early vision cues (or primitives) are fused in the visual cortex to compose complex shapes and descriptors. While different aspects of the process have been extensively studied, such as lens adaptation or feature detection, some other aspects, such as feature fusion, have been mostly left aside. In this work, we elaborate on the fusion of early vision primitives using generalizations of the Choquet integral, and novel aggregation operators that have been extensively studied in recent years. We propose to use generalizations of the Choquet integral to sensibly fuse elementary edge cues, in an attempt to model the behaviour of neurons in the early visual cortex. Our proposal leads to a fully-framed edge detection algorithm whose performance is put to the test in state-of-the-art edge detection datasets.Show more Publication Open Access d-XC integrals: on the generalization of the expanded form of the Choquet integral by restricted dissimilarity functions and their applications(IEEE, 2022) Wieczynski, Jonata; Fumanal Idocin, Javier; Lucca, Giancarlo; Borges, Eduardo N.; Da Cruz Asmus, Tiago; Emmendorfer, Leonardo R.; Bustince Sola, Humberto; Pereira Dimuro, Graçaliz; Automática y Computación; Automatika eta Konputazioa; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Restricted dissimilarity functions (RDFs) were introduced to overcome problems resulting from the adoption of the standard difference. Based on those RDFs, Bustince et al. introduced a generalization of the Choquet integral (CI), called d-Choquet integral, where the authors replaced standard differences with RDFs, providing interesting theoretical results. Motivated by such worthy properties, joint with the excellent performance in applications of other generalizations of the CI (using its expanded form, mainly), this paper introduces a generalization of the expanded form of the standard Choquet integral (X-CI) based on RDFs, which we named d-XC integrals. We present not only relevant theoretical results but also two examples of applications. We apply d-XC integrals in two problems in decision making, namely a supplier selection problem (which is a multi-criteria decision making problem) and a classification problem in signal processing, based on motor-imagery brain-computer interface (MI-BCI). We found that two d-XC integrals provided better results when compared to the original CI in the supplier selection problem. Besides that, one of the d-XC integrals performed better than any previous MI-BCI results obtained with this framework in the considered signal processing problem.Show more Publication Open Access Pre-aggregation functions: construction and an application(IEEE, 2015) Lucca, Giancarlo; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Callejas Bedregal, Benjamin; Mesiar, Radko; Kolesárová, Anna; Bustince Sola, Humberto; Automática y Computación; Automatika eta KonputazioaShow more In this work we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build pre-aggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators like the maximum and the Choquet integral.Show more Publication Open Access On the generalizations of the Choquet integral for application in FRBCs(Springer, 2021) Lucca, Giancarlo; Borges, Eduardo N.; Berri, Rafael A.; Emmendorfer, Leonardo R.; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more An effective way to cope with classification problems, among others, is by using Fuzzy Rule-Based Classification Systems (FRBCSs). These systems are composed by two main components, the Knowledge Base (KB) and the Fuzzy Reasoning Method (FRM). The FRM is responsible for performing the classification of new examples based on the information stored in the KB. A key point in the FRM is how the information given by the fired fuzzy rules is aggregated. Precisely, the aggregation function is the component that differs from the two most widely used FRMs in the specialized literature. In this paper we provide a revision of the literature discussing the generalizations of the Choquet integral that has been applied in the FRM of a FRBCS. To do so, we consider an analysis of different generalizations, by t-norms, copulas, and by F functions. Also, the main contributions of each generalization are discussed.Show more Publication Open Access Application of the Sugeno integral in fuzzy rule-based classification(Springer, 2022) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Fuzzy Rule-Based Classification System (FRBCS) is a well known technique to deal with classification problems. Recent studies have considered the usage of the Choquet integral and its generalizations to enhance the quality of such systems. Precisely, it was applied to the Fuzzy Reasoning Method (FRM) to aggregate the fired fuzzy rules when classify new data. On the other side, the Sugeno integral, another well known aggregation operator, obtained good results when applied to brain-computer interfaces. Those facts led to the present study in which we consider the Sugeno integral in classification problems. That is, the Sugeno integral is applied in the FRM of a widely used FRBCS and its performance is analyzed over 33 different datasets from the literature. In order to show the efficiency of this new approach, the obtained results are also compared to past studies involving the application of different aggregation functions. Finally, we perform a statistical analysis of the application.Show more