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 Matemáticas
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.
Open Access
Uso de t-normas para el estudio de la convexidad en conjuntos difusos intervalo-valuados
(Universidad de Málaga, 2021) Huidobro, Pedro; Alonso, Pedro; Bustince Sola, Humberto; Janis, Vladimír; Montes Rodríguez, Susana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En muchos problemas reales no se pueden tomar medidas de forma exacta. Así, los conjuntos difusos surgieron como una forma de intentar tratar con la incertidumbre de la forma más eficiente posible. Por otro lado, debe señalarse que la ‘convexidad es un concepto interesante en varias áreas dentro de las matemáticas. Teniendo esto en cuenta, en este documento proponemos una extensión del concepto de convexidad para conjuntos difusos intervalo-valuados basada en el uso de t-normas para intervalos. Para ello, y teniendo en consideración la literatura científica existente respecto de t-normas, presentamos una definición de t-norma aplicada a intervalos. Por último, comprobamos que nuestra definición de convexidad, utilizando t-normas, preserva la convexidad a través de intersecciones, es decir, que la intersección de dos conjuntos difusos intervalo-valuados convexos es también convexa.
Open Access
Cuantificar los hechos represivos: explicación y retos de la base de datos del fondo documental de la memoria histórica en Navarra
(2019) Majuelo Gil, Emilio; Mendiola Gonzalo, Fernando; Garmendia Amutxastegi, Gotzon; Piérola Narvarte, Gemma; García Funes, Juan Carlos; Yániz Berrio, Edurne; Pérez Ibarrola, Nerea; Barrenechea Tartas, Edurne; Rodríguez Martínez, Iosu; Sesma Redín, Rubén; Bustince Sola, Humberto; Ciencias Humanas y de la Educación; Giza eta Hezkuntza Zientziak; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este documento se presentan los fundamentos historiográficos y metodológicos de la base de datos del Fondo Documental de la Memoria Histórica en Navarra, desarrollada en la Universidad Pública de Navarra como consecuencia del encargo institucional realizado por el Parlamento y el Gobierno de Navarra. Con este fin, se ha procedido a elaborar una base de datos que permita una ágil consulta por parte de diferentes agentes sociales, institucionales y académicos en torno a la represión franquista, intentando incluir en ella la gran variedad de prácticas represivas que la historiografía ha ido identificando. Primeramente, se presenta un balance sobre la publicación, en los últimos años, de diferentes bases de datos on-line en torno a las víctimas de la guerra civil y la represión franquista en varias comunidades autónomas. A continuación, se presenta la unidad de análisis de nuestra base de datos, “los hechos represivos”, insertándola en el contexto historiográfico en torno a la represión franquista y los estudios sobre la violencia. En un tercer apartado pasamos a describir las diferentes categorías y subcategorías represivas en las que se enmarcan los hechos represivos, y finalmente se presentan algunas características técnicas de la organización interna de la información y el sofware de la base de datos.
Open Access
Hyperspectral imaging using notions from type-2 fuzzy sets
(Springer, 2019) López Maestresalas, Ainara; Miguel Turullols, Laura de; López Molina, Carlos; Arazuri Garín, Silvia; Bustince Sola, Humberto; Jarén Ceballos, Carmen; Ingeniería; Ingeniaritza; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Fuzzy set theory has developed a prolific armamentarium of mathematical tools for each of the topics that has fallen within its scope. One of such topics is data comparison, for which a range of operators has been presented in the past. These operators can be used within the fuzzy set theory, but can also be ported to other scenarios in which data are provided in various representations. In this work, we elaborate on notions for type-2 fuzzy sets, specifically for the comparison of type-2 fuzzy membership degrees, to create function comparison operators. We further apply these operators to hyperspectral imaging, in which pixelwise data are provided as functions over a certain energy spectra. The performance of the functional comparison operators is put to the test in the context of in-laboratory hyperspectral image segmentation.
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 Matematika
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.
Open Access
A generalization of the Choquet integral defined in terms of the Mobius transform
(IEEE, 2020) Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Horanská, Lubomíra; Mesiar, Radko; Stupñanová, Andrea; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this article, we propose a generalization of the Choquet integral, starting fromits definition in terms of the Mobius transform. We modify the product on R considered in the Lovasz extension form of the Choquet integral into a function F, and we discuss the properties of this new functional. For a fixed n, a complete description of all F yielding an n-ary aggregation function with a fixed diagonal section, independent of the considered fuzzy measure, is given, and several particular examples are presented. Finally, all functions F yielding an aggregation function, independent of the number n of inputs and of the considered fuzzy measure, are characterized, and related aggregation functions are shown to be just the Choquet integrals over the distorted inputs.
Open Access
On the notion of fuzzy dispersion measure and its application to triangular fuzzy numbers
(Elsevier, 2023) Roldán López de Hierro, Antonio Francisco; Bustince Sola, Humberto; Rueda, María del Mar; Roldán, Concepción; Miguel Turullols, Laura de; Guerra Errea, Carlos; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this paper, based on the analysis of the most widely used dispersion measure in the real context (namely, the variance), we introduce the notion of fuzzy dispersion measure associated to a finite set of data given by fuzzy numbers. This measure is implemented as a fuzzy number, so there is no loss of information caused by any defuzzification. The proposed concept satisfies the usual properties in a genuinely fuzzy sense and it avoids limitations in terms of its geometric shape or its analytical properties: under this conception, it could have a piece of its support in the negative part of the real line. This novel notion can be interpreted as a way of fusing the information included in a fuzzy data set in order to make a decision based on its dispersion. To illustrate the main characteristics of this approach, we present an example of a fuzzy dispersion measure that allows to conclude that this new way to deal this problem is coherent, at least, from the point of view of human intuition.
Open Access
Reduction of complexity using generators of pseudo-overlap and pseudo-grouping functions
(2024) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Zhang, Xiaohong; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Overlap and grouping functions can be used to measure events in which we must consider either the maximum or the minimum lack of knowledge. The commutativity of overlap and grouping functions can be dropped out to introduce the notions of pseudo-overlap and pseudo-grouping functions, respectively. These functions can be applied in problems where distinct orders of their arguments yield different values, i.e., in non-symmetric contexts. Intending to reduce the complexity of pseudo-overlap and pseudo-grouping functions, we propose new construction methods for these functions from generalized concepts of additive and multiplicative generators. We investigate the isomorphism between these families of functions. Finally, we apply these functions in an illustrative problem using them in a time series prediction combined model using the IOWA operator to evidence that using these generators and functions implies better performance.
Open Access
Operador de comparación de elementos multivaluados basado en funciones de equivalencia restringida
(Universidad de Málaga, 2021) Castillo López, Aitor; López Molina, Carlos; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este trabajo proponemos un nuevo enfoque del algoritmo de clustering gravitacional basado en lo que Einstein considero su 'mayor error': la constante cosmológica. De manera similar al algoritmo de clustering gravitacional, nuestro enfoque está inspirado en principios y leyes del cosmos, y al igual que ocurre con la teoría de la relatividad de Einstein y la teoría de la gravedad de Newton, nuestro enfoque puede considerarse una generalización del agrupamiento gravitacional, donde, el algoritmo de clustering gravitacional se recupera como caso límite. Además, se desarrollan e implementan algunas mejoras que tienen como objetivo optimizar la cantidad de iteraciones finales, y de esta forma, se reduce el tiempo de ejecución tanto para el algoritmo original como para nuestra versión.
Embargo
Fuzzy dissimilarities and the fuzzy choquet integral of triangular fuzzy numbers on [0,1]
(Elsevier, 2025-04-01) Roldán López de Hierro, Antonio Francisco; Cruz, Anderson; Santiago, Regivan; Roldán, Concepción; García-Zamora, Diego; Neres, Fernando; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Having in mind the huge amount of data daily registered in the world, it is becoming increasingly important to summarize the information included in a data set. In Statistics and Computer Science, this task is successfully carried out by aggregation functions. One of the most widely applied methodologies of aggregating data is the Choquet integral. The main aim of this paper is to introduce an appropriate notion of Choquet integral in the context of fuzzy numbers. To do this, we face three challenges: the underlying uncertainty when handling fuzzy numbers, the way to order fuzzy numbers by appropriate binary relations and the way to compute the dissimilarity among fuzzy numbers. Illustrative examples are given by involving the α-order on the family of all triangular fuzzy numbers with support on [0,1].