Open Access
Interval-valued aggregation functions based on moderate deviations applied to motor-imagery-based brain computer interface
(IEEE, 2021) Fumanal Idocin, Javier; Takáč, Zdenko; Fernández Fernández, Francisco Javier; Sanz Delgado, José Antonio; Goyena Baroja, Harkaitz; Lin, Chin-Teng; Wang, Yu-Kai; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this work we develop moderate deviation functions to measure similarity and dissimilarity among a set of given interval-valued data to construct interval-valued aggregation functions, and we apply these functions in two MotorImagery Brain Computer Interface (MI-BCI) systems to classify electroencephalography signals. To do so, we introduce the notion of interval-valued moderate deviation function and, in particular, we study those interval-valued moderate deviation functions which preserve the width of the input intervals. In order to apply them in a MI-BCI system, we first use fuzzy implication operators to measure the uncertainty linked to the output of each classifier in the ensemble of the system, and then we perform the decision making phase using the new interval-valued aggregation functions. We have tested the goodness of our proposal in two MI-BCI frameworks, obtaining better results than those obtained using other numerical aggregation and interval-valued OWA operators, and obtaining competitive results versus some non aggregation-based frameworks.
Open Access
Extensión multidimensional de la integral de Choquet discreta y su aplicación en redes neuronales recurrentes
(Universidad de Málaga, 2021) Ferrero Jaurrieta, Mikel; Rodríguez Martínez, Iosu; Pereira Dimuro, Graçaliz; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este trabajo presentamos una definición de la integral de Choquet discreta n-dimensional, para fusionar datos vectoriales. Como aplicación, utilizamos estas nuevas integrales de Choquet discretas multidimensionales en la fusión de información secuencial en las redes neuronales recurrentes, mejorando los resultados obtenidos mediante el método de agregación tradicional.
Open Access
F-homogeneous functions and a generalization of directional monotonicity
(Wiley, 2022) Santiago, Regivan; Sesma Sara, Mikel; Fernández Fernández, Francisco Javier; Takáč, Zdenko; Mesiar, Radko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
A function that takes (Formula presented.) numbers as input and outputs one number is said to be homogeneous whenever the result of multiplying each input by a certain factor (Formula presented.) yields the original output multiplied by that same factor. This concept has been extended by the notion of abstract homogeneity, which generalizes the product in the expression of homogeneity by a general function (Formula presented.) and the effect of the factor (Formula presented.) by an automorphism. However, the effect of parameter (Formula presented.) remains unchanged for all the input values. In this study, we generalize further the condition of abstract homogeneity by introducing (Formula presented.) -homogeneity, which is defined with respect to a family of functions, enabling a different behavior for each of the inputs. Next, we study the properties that are satisfied by this family of functions and, moreover, we link this concept with the condition of directional monotonicity, which is a trendy property in the framework of aggregation functions. To achieve that, we generalize directional monotonicity by (Formula presented.) directional monotonicity, which is defined with respect to a family of functions (Formula presented.) and a family of vectors (Formula presented.). Finally, we show how the introduced concepts could be applied in two different problems of computer vision: a snow detection problem and image thresholding improvement. © 2022 The Authors. International Journal of Intelligent Systems published by Wiley Periodicals LLC.
Open Access
Fuzzy sets complement-based gated recurrent unit
(CEUR Workshop Proceedings (CEUR-WS.org), 2021) Ferrero Jaurrieta, Mikel; Pereira Dimuro, Graçaliz; Takáč, Zdenko; Santiago, Regivan; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Gobierno de Navarra / Nafarroako Gobernua
Gated Recurrent Units (GRU) are neural network gated architectures that simplify other ones (suchas, LSTM) by joining gates mainly. For this, instead of using two gates, if𝑥is the first gate, standardoperation1−𝑥is used to generate the second one, optimizing the number of parameters. In this work, we interpret this information as a fuzzy set, and we generalize the standard operation using fuzzy negations, and improving the accuracy obtained with the standard one.
Unknown
Ordered directional monotonicity in the construction of edge detectors
(Elsevier, 2021) Marco Detchart, Cedric; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Mesiar, Radko; Lafuente López, Julio; Barrenechea Tartas, Edurne; Pintor Borobia, Jesús María; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería
In this paper we provide a specific construction method of ordered directionally monotone functions. We show that the functions obtained with this construction method can be used to build edge detectors for grayscale images. We compare the results of these detectors to those obtained with some other ones that are widely used in the literature. Finally, we show how a consensus edge detector can be built improving the results obtained both by our proposal and by those in the literature when applied individually.
Open Access
A generalization of the gravitational search algorithm
(Springer, 2017-05-19) Bustince Sola, Humberto; Minárová, María; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Marco Detchart, Cedric; Ruiz-Aranguren, Javier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
In this work we propose a generalization of the gravitational search algorithm where the product in the expression of the gravitational attraction force is replaced by more general functions. We study some conditions which ensure convergence of our proposal and we show that we recover a wide class of aggregation functions to replace the product.
Open Access
Supervised penalty-based aggregation applied to motor-imagery based brain-computer-interface
(Elsevier, 2024) Fumanal Idocin, Javier; Vidaurre Arbizu, Carmen; Fernández Fernández, Francisco Javier; Gómez Fernández, Marisol; Andreu-Pérez, Javier; Prasad, M.; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute of Smart Cities - ISC
In this paper we propose a new version of penalty-based aggregation functions, the Multi Cost Aggregation choosing functions (MCAs), in which the function to minimize is constructed using a convex combination of two relaxed versions of restricted equivalence and dissimilarity functions instead of a penalty function. We additionally suggest two different alternatives to train a MCA in a supervised classification task in order to adapt the aggregation to each vector of inputs. We apply the proposed MCA in a Motor Imagery-based Brain- Computer Interface (MI-BCI) system to improve its decision making phase. We also evaluate the classical aggregation with our new aggregation procedure in two publicly available datasets. We obtain an accuracy of 82.31% for a left vs. right hand in the Clinical BCI challenge (CBCIC) dataset, and a performance of 62.43% for the four-class case in the BCI Competition IV 2a dataset compared to a 82.15% and 60.56% using the arithmetic mean. Finally, we have also tested the goodness of our proposal against other MI-BCI systems, obtaining better results than those using other decision making schemes and Deep Learning on the same datasets.
Open Access
Affine construction methodology of aggregation functions
(Elsevier, 2020) Roldán López de Hierro, Antonio Francisco; Roldán, Concepción; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Rodríguez Martínez, Iosu; Fardoun, Habib; Lafuente López, Julio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Aggregation functions have attracted much attention in recent times because of its potential use in many areas such us data fusion and decision making. In practice, most of the aggregation functions that scientists use in their studies are constructed from very simple (usually affine or polynomial) functions. However, these are distinct in nature. In this paper, we develop a systematic study of these two classes of functions from a common point of view. To do this, we introduce the class of affine aggregation functions, which cover both the aforementioned families and most of examples of aggregation functions that are used in practice, including, by its great applicability, the symmetric case. Our study allows us to characterize when a function constructed from affine or polynomial functions is, in fact, a new aggregation function. We also study when sums or products of this kind of functions are again an aggregation function.
Open Access
On fuzzy implications derived from general overlap functions and their relation to other classes
(MDPI, 2023) Pinheiro, Jocivania; Santos, Helida; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Santiago, Regivan; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO, N)-implication functions. We also investigate their properties, the aggregation of (GO, N)-implication functions, their characterization and the intersections with other classes of fuzzy implication functions.
Open Access
Hyperspectrum comparison using similarity measures
(IEEE, 2017-08-31) López Molina, Carlos; Marco Detchart, Cedric; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; López Maestresalas, Ainara; Ayala Martini, Daniela; Automática y Computación; Automatika eta Konputazioa; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta Proiektuak
Similarity measures, as studied in the context of fuzzy set theory, have been proven applicable to many different fields. Surely, their primary role is to model the perceived (dis-) similarity between two fuzzy sets or, equivalently, the linguistic terms they represent. However, the richness of the dedicated study makes the similarity measures portable to other contexts in which quantitative comparison plays a key role. In this work we present the application of similarity measures to hyperspectrum comparison in the context of in-lab hyperspectral imaging for bioengineering.