# 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 General grouping functions(Springer, 2020) Santos, Helida; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Sanz Delgado, José Antonio; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasShow more Some aggregation functions that are not necessarily associative, namely overlap and grouping functions, have called the attention of many researchers in the recent past. This is probably due to the fact that they are a richer class of operators whenever one compares with other classes of aggregation functions, such as t-norms and t-conorms, respectively. In the present work we introduce a more general proposal for disjunctive n-ary aggregation functions entitled general grouping functions, in order to be used in problems that admit n dimensional inputs in a more flexible manner, allowing their application in different contexts. We present some new interesting results, like the characterization of that operator and also provide different construction methods.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 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 T-overlap t-migrative functions: a generalization of migrativity in t-overlap functions(Universidad Distrital Francisco José de Caldas (Colombia), 2020) Zapata, Hugo; Bustince Sola, Humberto; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Este artículo introduce una generalización de funciones migrativas por extensión de la condición de la operación producto aplicada en las variables. Más específicamente, en lugar de exigir multiplicar la variable x por un número real alfa; en este trabajo se trabaja este número alfa con las variables de acuerdo a una t-norma. Se denomina a esta generalización función t-migrativa con respecto a tal tnorma. Luego se analizan las propiedades principales de funciones t-migrativas en funciones t-overlap y se introducen algunos métodos de construcción de este tipo de funciones.Show more Publication Open Access Multimodal fuzzy fusion for enhancing the motor-imagery-based brain computer interface(IEEE, 2019) Ko, Li-Wei; Lu, Yi-Chen; Bustince Sola, Humberto; Chang, Yu-Cheng; Chang, Yang; Fernández Fernández, Francisco Javier; Wang, Yu-Kai; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Lin, Chin-Teng; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasShow more Brain–computer interface technologies, such as steady-state visually evoked potential, P300, and motor imagery are methods of communication between the human brain and the external devices. Motor imagery–based brain–computer interfaces are popular because they avoid unnecessary external stimulus. Although feature extraction methods have been illustrated in several machine intelligent systems in motor imagery-based brain–computer interface studies, the performance remains unsatisfactory. There is increasing interest in the use of the fuzzy integrals, the Choquet and Sugeno integrals, that are appropriate for use in applications in which fusion of data must consider possible data interactions. To enhance the classification accuracy of brain-computer interfaces, we adopted fuzzy integrals, after employing the classification method of traditional brain–computer interfaces, to consider possible links between the data. Subsequently, we proposed a novel classification framework called the multimodal fuzzy fusion-based brain-computer interface system. Ten volunteers performed a motor imagery-based brain-computer interface experiment, and we acquired electroencephalography signals simultaneously. The multimodal fuzzy fusion-based brain-computer interface system enhanced performance compared with traditional brain–computer interface systems. Furthermore, when using the motor imagery-relevant electroencephalography frequency alpha and beta bands for the input features, the system achieved the highest accuracy, up to 78.81% and 78.45% with the Choquet and Sugeno integrals, respectively. Herein, we present a novel concept for enhancing brain–computer interface systems that adopts fuzzy integrals, especially in the fusion for classifying brain–computer interface commands.Show more Publication Open Access Applying d-XChoquet integrals in classification problems(IEEE, 2022) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Emmendorfer, Leonardo R.; Ferrero Jaurrieta, Mikel; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS's) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.Show more Publication Embargo A generalization of the Sugeno integral to aggregate interval-valued data: an application to brain computer interface and social network analysis(Elsevier, 2022) Fumanal Idocin, Javier; Takáč, Zdenko; Horanská, Lubomíra; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Vidaurre Arbizu, Carmen; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Institute of Smart Cities - ISCShow more Intervals are a popular way to represent the uncertainty related to data, in which we express the vagueness of each observation as the width of the interval. However, when using intervals for this purpose, we need to use the appropriate set of mathematical tools to work with. This can be problematic due to the scarcity and complexity of interval-valued functions in comparison with the numerical ones. In this work, we propose to extend a generalization of the Sugeno integral to work with interval-valued data. Then, we use this integral to aggregate interval-valued data in two different settings: first, we study the use of intervals in a brain-computer interface; secondly, we study how to construct interval-valued relationships in a social network, and how to aggregate their information. Our results show that interval-valued data can effectively model some of the uncertainty and coalitions of the data in both cases. For the case of brain-computer interface, we found that our results surpassed the results of other interval-valued functions.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 Generalizing max pooling via (a, b)-grouping functions for convolutional neural networks(Elsevier, 2023) Rodríguez Martínez, Iosu; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Herrera, Francisco; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more Due to their high adaptability to varied settings and effective optimization algorithm, Convolutional Neural Networks (CNNs) have set the state-of-the-art on image processing jobs for the previous decade. CNNs work in a sequential fashion, alternating between extracting significant features from an input image and aggregating these features locally through ‘‘pooling" functions, in order to produce a more compact representation. Functions like the arithmetic mean or, more typically, the maximum are commonly used to perform this downsampling operation. Despite the fact that many studies have been devoted to the development of alternative pooling algorithms, in practice, ‘‘max-pooling" still equals or exceeds most of these possibilities, and has become the standard for CNN construction. In this paper we focus on the properties that make the maximum such an efficient solution in the context of CNN feature downsampling and propose its replacement by grouping functions, a family of functions that share those desirable properties. In order to adapt these functions to the context of CNNs, we present (𝑎��, 𝑏��)- grouping functions, an extension of grouping functions to work with real valued data. We present different construction methods for (𝑎, 𝑏)-grouping functions, and demonstrate their empirical applicability for replacing max-pooling by using them to replace the pooling function of many well-known CNN architectures, finding promising results.Show more Publication Open Access Funções de agregação baseadas em integral de Choquet aplicadas em redimensionalização de imagens(Universidade Passo Fundo, 2019) Bueno, Jéssica C. S.; Dias, Camila A.; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Botelho, Silvia S. C.; Mattos, Viviane L. D. de; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more The increasing data volume, coupled with the high complexity of these data, has generated the need to develop increasingly efficient knowledge extraction techniques, both in computational cost and precision. Most of the problems that are addressed by these techniques have complex information to be identified. For this, machine learning methods are used, where these methods use a variety of functions inside the different steps that are employed in their architectures. One of these consists in the use of aggregation functions to resize images. In this context, a study of aggregation functions based on the Choquet integral is presented, where the main feature of Choquet integral, in comparison with other aggregation functions, resides in the fact that it considers, through the fuzzy measure, the interaction between the elements to be aggregated. Thus, an evaluation study of the performance of the standard Choquet integral functions is presented (Choquet integral based on Copula in relation to the maximum and average functions) looking for results that may be better than the usual applied aggregation functions. The results of such comparisons are promising when evaluated through measures of image quality.Show more