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
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; Bedregal, Benjamin; Takáč, Zdenko; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13
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.
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
Análisis de redes sociales basado en las conquistas de César Borgia
(Universidad de Málaga, 2021) Fumanal Idocin, Javier; Cordón, Óscar; Alonso Betanzos, Amparo; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este trabajo presentamos el modelado de redes sociales y detección de comunidades utilizando como base un evento histórico real, las conquistas de César Borgia en el siglo XV. Para ello, proponemos un nuevo conjunto de funciones, llamadas funciones de afinidad, disenadas para capturar la 'naturaleza de las interacciones locales entre cada par de actores en una red. Utilizando estas funciones, desarrollamos un nuevo algoritmo de detección de comunidades, el Borgia Clustering, donde las comunidades surgen naturalmente de un proceso de simulación de interacción de múltiples agentes en la red. También discutimos los efectos del tamaño y la escala de cada comunidad, y como pueden ser tomadas en cuenta en el proceso de simulación. Finalmente, comparamos nuestra detección de comunidades con otros algoritmos representativos, encontrando resultados favorables a nuestra propuesta.
Open Access
Mixture functions and their monotonicity
(Elsevier, 2019) Špirková, Jana; Beliakov, Gleb; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
We consider mixture functions, which are a type of weighted averages for which the corresponding weights are calculated by means of appropriate continuous functions of their inputs. In general, these mixture function need not be monotone increasing. For this reason we study su cient conditions to ensure standard, weak and directional monotonicity for speci c types of weighting functions. We also analyze directional monotonicity when di erentiability is assumed.
Open Access
Paired structures in knowledge representation
(Elsevier, 2016) Montero, Javier; Bustince Sola, Humberto; Pagola Barrio, Miguel; Fernández Fernández, Francisco Javier; Barrenechea Tartas, Edurne; Automática y Computación; Automatika eta Konputazioa
In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here it is claimed that it is the semantic relationship between two paired concepts what determines the emergence of different types of neutrality, namely indeterminacy, ambivalence and conflict, widely used under different frameworks (possibly under different names). It will be shown the potential relevance of paired structures, generated from two paired concepts together with their associated neutrality, all of them to be modeled as fuzzy sets. In this way, paired structures can be viewed as a standard basic model from which different models arise. This unifying view should therefore allow a deeper analysis of the relationships between several existing knowledge representation formalisms, providing a basis from which more expressive models can be later developed.
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.
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.
Embargo
Construction methods of fuzzy implications on bounded posets
(Elsevier, 2024) Wang, Mei; Zhang, Xiaohong; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
The fuzzy implication on bounded lattices was introduced by Palmeira et al., and the method of extending fuzzy implications on bounded lattices by using retraction was provided. However, we find that the extension of fuzzy implications on bounded lattices can also be realized through homomorphism. In order to get better results, we will continue to study this topic in this paper. In particular, we will focus on the construction methods of fuzzy implications on bounded posets. More precisely, we will give some construction methods of fuzzy implications via 0,1-homomorphism on bounded posets. Then we further study two special kinds of fuzzy implications, (Q,N)-implications and RQ-implications on bounded posets, where Q is a quasi-overlap function. Finally, we discuss the distributive laws and the importation laws of (Q,N)-implications and RQ-implications over a quasi-overlap function Q.
Open Access
The null space of fuzzy inclusion measures
(IEEE, 2019) Couso, Inés; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Sánchez, Luciano; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Some formal relationships between the different axiomatic definitions of inclusion measure are analysed. In particular, the links between the different proposals about the null-space (the collection of pairs associated with a null degree of inclusion) are studied. Taking as starting point the well-known axiomatics of Kitainik and Sinha-Dougherty, we observe that other alternative proposals about the null-space are incompatible with both the null-space and the decomposition axioms of these authors. We also conclude that both the axiomatics of Kitainik and that of Sinha-Dougherty contain certain redundancies. Reduced equivalent lists of axioms are proposed.