Open Access
Funciones de agregación inspiradas en la integral Choquet
(CAEPIA, 2024) Bustince Sola, Humberto; Lafuente López, Julio; González García, Xabier; Pereira Dimuro, Graçaliz; Mesiar, Radko; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
En este trabajo presentamos una nueva clase de funciones de agregación. Para la definición de estas nuevas funciones nos inspiramos en el método de construcción de las integrales Choquet, reemplazando las medidas por funciones adecuadas. Tras discutir la definición de las nuevas funciones, estudiamos algunas de su propiedades básicas y consideramos su relación con otras funciones de agregación utilizadas en la literatura, como los estadísticos de orden o las funciones de overlap y grouping.
Open Access
The lattice of fitting classes which are right extensible by soluble groups
(Universidad Autónoma de Barcelona, Departamento de Matemáticas, 2005) Iranzo, M.J.; Lafuente López, Julio; Pérez Monasor, F.; Matemáticas; Matematika
In this paper we study the set of fitting classes which are right extensible by soluble groups ordered by the inclusion relation. The consideration of the associated lattices gives rise to new fitting classes and it allows to obtain some injectivity criteria for general fitting classes.
Open Access
Los retículos de las clases de Schunck normales y de las clases derivadas
(Real Sociedad Matemática Española, 1979) Lafuente López, Julio; Matemáticas; Matematika
All groups to be considered are finite. The main result of this paper is the following: the normal Schunck classes compose a complete and distributive lattice antiisomorphic to the lattice composed by the derived classes. It begins with a first section of machinery which establishes that the derived classes are precisely the classes of groups G such that every simple section of G appartains to a σ-closed class of simple groups; therefore the derived classes are a natural generalization of the classes of σ-groups. Finally we study the lattice properties of the normal Schunck classes relative to a class of groups.
Open Access
Strengthened ordered directional and other generalizations of monotonicity for aggregation functions
(Springer, 2018) Sesma Sara, Mikel; Miguel Turullols, Laura de; Lafuente López, Julio; Barrenechea Tartas, Edurne; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
A tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss strengthened ordered directional monotonicity, its relation to other types of monotonicity, such as directional and ordered directional monotonicity and the main properties of the class of functions that are strengthened ordered directionally monotone. We also study some construction methods for such functions and provide a characterization of usual monotonicity in terms of these notions of monotonicity.
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
Interval subsethood measures with respect to uncertainty for the interval-valued fuzzy setting
(Atlantis Press, 2020) Pekala, Barbara; Bentkowska, Urszula; Sesma Sara, Mikel; Fernández Fernández, Francisco Javier; Lafuente López, Julio; Altalhi, A. H.; Knap, Maksymilian; Bustince Sola, Humberto; Pintor Borobia, Jesús María; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería
In this paper, the problem of measuring the degree of subsethood in the interval-valued fuzzy setting is addressed. Taking into account the widths of the intervals, two types of interval subsethood measures are proposed. Additionally, their relation and main properties are studied. These developments are made both with respect to the regular partial order of intervals and with respect to admissible orders. Finally, some construction methods of the introduced interval subsethood measures with the use interval-valued aggregation functions are examined.
Open Access
Grupos primitivos con subgrupos maximales pequeños
(Universidad Autónoma de Barcelona, Departamento de Matemáticas, 1985) Lafuente López, Julio; Matemáticas; Matematika
Open Access
Curve-based monotonicity: a generalization of directional monotonicity
(Taylor & Francis, 2019) Roldán López de Hierro, Antonio Francisco; Sesma Sara, Mikel; Špirková, Jana; Lafuente López, Julio; Pradera, Ana; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this work we propose a generalization of the notion of directional monotonicity. Instead of considering increasingness or decreasingness along rays, we allow more general paths defined by curves in the n-dimensional space. These considerations lead us to the notion of α-monotonicity, where α is the corresponding curve. We study several theoretical properties of α-monotonicity and relate it to other notions of monotonicity, such as weak monotonicity and directional monotonicity.
Open Access
Reemplazo de la función de pooling de redes neuronales convolucionales por combinaciones lineales de funciones crecientes
(Universidad de Málaga, 2021) Rodríguez Martínez, Iosu; Lafuente López, Julio; Sesma Sara, Mikel; Herrera, Francisco; Ursúa Medrano, Pablo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Las redes convolucionales llevan a cabo un proceso automatico de extracción y fusión de características mediante el cual obtienen la información más relevante de una imagen dada. El proceso de submuestreo mediante el cual se fusionan características localmente próximas, conocido como ‘pooling’, se lleva a cabo tradicionalmente con funciones sencillas como el máximo o la media aritmética, ignorando otras opciones muy populares en el campo de la teoría de agregaciones. En este trabajo proponemos reemplazar dichas funciones por otra serie de ordenes estadísticos, así como por la integral de Sugeno y una nueva generalización de la misma. Además, basándonos en trabajos que emplean la combinación convexa del máximo y la media, presentamos una nueva capa que permite combinar varias de las nuevas agregaciones, mejorando sus resultados individuales.
Open Access
La matemática: definiciones y modelos
(Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, 2005) Lafuente López, Julio; Matemáticas; Matematika