Open Access
Using the Choquet integral in the fuzzy reasoning method of fuzzy rule-based classification systems
(MDPI, 2013) Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Paternain Dallo, Daniel; Sanz Delgado, José Antonio; Automática y Computación; Automatika eta Konputazioa
In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the new method with the same fuzzy measure for all the classes. However, the relationship among the set of rules of each class can be different and therefore the best fuzzy measure can change depending on the class. Consequently, we propose a learning method by means of a genetic algorithm in which the most suitable fuzzy measure for each class is computed. From the obtained results it is shown that our new proposal allows the performance of the classical fuzzy reasoning methods of the winning rule and additive combination to be enhanced whenever the fuzzy measure is appropriate for the tackled problem.
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
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
A new family of aggregation functions for intervals
(Springer, 2024) Díaz-Vázquez, Susana; Torres-Manzanera, Emilio; Rico, Noelia; Mesiar, Radko; Rodríguez Martínez, Iosu; Lafuente López, Julio; Díaz, Irene; Montes Rodríguez, Susana; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Aggregation operators are unvaluable tools when different pieces of information have to be taken into account with respect to the same object. They allow to obtain a unique outcome when different evaluations are available for the same element/object. In this contribution we assume that the opinions are not given in form of isolated values, but intervals. We depart from two “classical” aggregation functions and define a new operator for aggregating intervals based on the two original operators. We study under what circumstances this new function is well defined and we provide a general characterization for monotonicity. We also study the behaviour of this operator when the departing functions are the most common aggregation operators. We also provide an illustrative example demonstrating the practical application of the theoretical contribution to ensemble deep learning models.
Open Access
Orderings in the referential set induced by intuitionistic fuzzy relation
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Burillo López, Pedro; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this paper we present different orderings in the referential set induced by intuitionistic fuzzy relations of ordering. We can see how these induced orders justify the definition given of intuitionistic fuzzy antisymmetry and the definition of partial enclosure.
Open Access
Type-2 fuzzy entropy-sets
(IEEE, 2017) Miguel Turullols, Laura de; Santos, Helida; Sesma Sara, Mikel; Bedregal, Benjamin; Jurío Munárriz, Aránzazu; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with Type-2 Fuzzy Sets. We denote this concept Type-2 Fuzzy Entropy-Set. However, the construction of the notion of entropy measure on an infinite set, such us [0, 1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a Fuzzy Set on the universe [0, 1]. Furthermore, whenever the membership function of the considered Fuzzy Set in the universe [0, 1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca y Termini. Finally, we present an illustrative example where we use Type-2 Fuzzy Entropy-Sets instead of fuzzy entropies in a classical fuzzy algorithm.
Open Access
Type-(2, k) overlap indices
(IEEE, 2022) Roldán López de Hierro, Antonio Francisco; Roldán, Concepción; Tíscar, Miguel Ángel; Takáč, Zdenko; Santiago, Regivan; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Automatic image detection is one of the most im- portant areas in computing due to its potential application in numerous real-world scenarios. One important tool to deal with that is called overlap indices. They were introduced as a procedure to provide the maximum lack of knowledge when comparing two fuzzy objects. They have been successfully applied in the following fields: image processing, fuzzy rule-based systems, decision making and computational brain interfaces. This notion of overlap indices is also necessary for applications in which type-2 fuzzy sets are required. In this paper we introduce the notion of type-(2, k) overlap index (k 0, 1, 2) in the setting of type-2 fuzzy sets. We describe both the reasons that have led to this notion and the relationships that naturally arise among the algebraic underlying structures. Finally, we illustrate how type- (2, k) overlap indices can be employed in the setting of fuzzy rule-based systems when the involved objects are type-2 fuzzy sets.
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
On the influence of interval normalization in IVOVO fuzzy multi-class classifier
(Springer, 2019) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13
IVOVO stands for Inverval-Valued One-Vs-One and is the combination of IVTURS fuzzy classifier and the One-Vs-One strategy. This method is designed to improve the performance of IVTURS in multi-class problems, by dividing the original problem into simpler binary ones. The key issue with IVTURS is that interval-valued confidence degrees for each class are returned and, consequently, they have to be normalized for applying a One-Vs-One strategy. However, there is no consensus on which normalization method should be used with intervals. In IVOVO, the normalization method based on the upper bounds was considered as it maintains the admissible order between intervals and also the proportion of ignorance, but no further study was developed. In this work, we aim to extend this analysis considering several normalizations in the literature. We will study both their main theoretical properties and empirical performance in the final results of IVOVO.
Open Access
Learning ordered pooling weights in image classification
(Elsevier, 2020) Forcén Carvalho, Juan Ignacio; Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Spatial pooling is an important step in computer vision systems like Convolutional Neural Networks or the Bag-of-Words method. The spatial pooling purpose is to combine neighbouring descriptors to obtain a single descriptor for a given region (local or global). The resultant combined vector must be as discriminant as possible, in other words, must contain relevant information, while removing irrelevant and confusing details. Maximum and average are the most common aggregation functions used in the pooling step. To improve the aggregation of relevant information without degrading their discriminative power for image classification, we introduce a simple but effective scheme based on Ordered Weighted Average (OWA) aggregation operators. We present a method to learn the weights of the OWA aggregation operator in a Bag-of-Words framework and in Convolutional Neural Networks, and provide an extensive evaluation showing that OWA based pooling outperforms classical aggregation operators.