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
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 los cambios en los patrones de temperatura mediante técnicas de stream clustering
(CAEPIA, 2024) Urío Larrea, Asier; Pereira Dimuro, Graçaliz; Andreu-Pérez, Javier; Camargo, Heloisa A.; Aguirre Eraso, Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
El cambio climático afecta a las condiciones medioambientales de las distintas regiones. La capacidad de constatar estos cambios es una eficaz herramienta para adaptarse a la evolución de las condiciones. Los datos meteorológicos se generan continuamente en múltiples estaciones de todo el mundo, proporcionando una valiosa información sobre la variabilidad en el tiempo de los patrones climáticos. El estudio de este flujo de datos nos permite comprender mejor los nuevos patrones climáticos. Este trabajo explora, mediante un algoritmo de agrupamiento de flujos de datos (stream clustering), el potencial de emplear datos meteorológicos obtenidos en diferentes localizaciones geográficas para rastrear el cambio en los patrones climáticos en la Comunidad Foral de Navarra durante los últimos 20 años. El estudio de caso mostró la aplicabilidad de los métodos de flujos de datos a la segmentación incremental de regiones geográficas en función de sus factores climatológicos.
Open Access
The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions
(Elsevier, 2019) Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Pintor Borobia, Jesús María; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería
Overlap and grouping functions are special kinds of non necessarily associative aggregation operators proposed for many applications, mainly when the associativity property is not strongly required. The classes of overlap and grouping functions are richer than the classes of t-norms and t-conorms, respectively, concerning some properties like idempotency, homogeneity, and, mainly, the self-closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap/grouping functions. In previous works, we introduced some classes of fuzzy implications derived by overlap and/or grouping functions, namely, the residual implications R-0-implications, the strong implications (G, N)-implications and the Quantum Logic implications QL-implications, for overlap functions O, grouping functions G and fuzzy negations N. Such implications do not necessarily satisfy certain properties, but only weaker versions of these properties, e.g., the exchange principle. However, in general, such properties are not demanded for many applications. In this paper, we analyze the so-called law of O-Conditionality, O(x, 1(x, y)) <= y, for any fuzzy implication I and overlap function O, and, in particular, for Ro-implications, (G, N)-implications, QL-implications and D-implications derived from tuples (O, G, N), the latter also introduced in this paper. We also study the conditional antecedent boundary condition for such fuzzy implications, since we prove that this property, associated to the left ordering property, is important for the analysis of the O-Conditionality. We show that the use of overlap functions to implement de generalized Modus Ponens, as the scheme enabled by the law of O-Conditionality, provides more generality than the laws of T-conditionality and U-conditionality, for t-norms T and uninorms U, respectively.
Open Access
CC-separation measure applied in business group decision making
(SciTePress, 2021) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Pereira Dimuro, Graçaliz; Lourenzutti, Rodolfo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In business, one of the most important management functions is decision making The Group Modular Choquet Random TOPSIS (GMC-RTOPSIS) is a Multi-Criteria Decision Making (MCDM) method that can work with multiple heterogeneous data types. This method uses the Choquet integral to deal with the interaction between different criteria. The Choquet integral has been generalized and applied in various fields of study, such as imaging processing, brain-computer interface, and classification problems. By generalizing the so-called extended Choquet integral by copulas, the concept of CC-integrals has been introduced, presenting satisfactory results when used to aggregate the information in Fuzzy Rule-Based Classification Systems. Taking this into consideration, in this paper. we applied 11 different CC-integrals in the GMC-RTOPSIS. The results demonstrated that this approach has the advantage of allowing more flexibility and certainty in the choosing process by giving a higher separation between the first and second-ranked alternatives.
Open Access
Quantifying external information in social network analysis: an application to comparative mythology
(IEEE, 2023) Fumanal Idocin, Javier; Cordón García, Óscar; Pereira Dimuro, Graçaliz; Roldán López de Hierro, Antonio Francisco; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Social network analysis is a popular tool to understand the relationships between interacting agents by studying the structural properties of their connections. However, this kind of analysis can miss some of the domain-specific knowledge available in the original information domain and its propagation through the associated network. In this work, we develop an extension of classical social network analysis to incorporate external information from the original source of the network. With this extension we propose a new centrality measure, the semantic value, and a new affinity function, the semantic affinity, that establishes fuzzy-like relationships between the different actors in the network. We also propose a new heuristic algorithm based on the shortest capacity problem to compute this new function. As an illustrative case study, we use the novel proposals to analyze and compare the gods and heroes from three different classical mythologies: 1) Greek; 2) Celtic; and 3) Nordic. We study the relationships of each individual mythology and those of the common structure that is formed when we fuse the three of them. We also compare our results with those obtained using other existing centrality measures and embedding approaches. In addition, we test the proposed measures on a classical social network, the Reuters terror news network, as well as in a Twitter network related to the COVID-19 pandemic. We found that the novel method obtains more meaningful comparisons and results than previous existing approaches in every case.
Open Access
The evolution of the notion of overlap functions
(Springer, 2021) Bustince Sola, Humberto; Mesiar, Radko; Pereira Dimuro, Graçaliz; Fernández Fernández, Francisco Javier; Bedregal, Benjamin; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this chapter we make a review of the notion of overlap function. Although originally developed in order to determine up to what extent a given element belongs to two sets, overlap functions have widely developed in the last years for very different problems. We recall here the motivation that led to the introduction of this new notion and we discuss further theoretical developments that have appeared to deal with other types of problems.
Open Access
Application of the Sugeno integral in fuzzy rule-based classification
(Elsevier, 2024-09-27) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Urío Larrea, Asier; López Molina, Carlos; Bustince Sola, Humberto; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Fuzzy Rule-Based Classification System (FRBCS) is a well-known technique to deal with classification problems. Recent studies have considered the usage of the Choquet integral and its generalizations (e.g.: 𝐶𝑇 -integral, 𝐶𝐹 - Integral and 𝐶𝐶-integral) to enhance the performance of such systems. Such fuzzy integrals were applied to the Fuzzy Reasoning Method (FRM) to aggregate the fired fuzzy rules when classifying new data. However, the Sugeno integral, another well-known aggregation operator, obtained good results in other applications, such as brain–computer interfaces. These facts led to the present study, in which we consider the Sugeno integral in classification problems. That is, the Sugeno integral is applied in the FRM of a widely used FRBCS, and its performance is analyzed over 33 different datasets from the literature, also considering different fuzzy measures. To show the efficiency of this new approach, the results obtained are also compared with previous studies that involved the application of different aggregation functions. Finally, we perform a statistical analysis of the application.
Open Access
Enhancing LSTM for sequential image classification by modifying data aggregation
(IEEE, 2021) Takáč, Zdenko; Ferrero Jaurrieta, Mikel; Horanská, Lubomíra; Krivonakova, Nada; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Recurrent Neural Networks (RNN) model sequential information and are commonly used for the analysis of time series. The most usual operation to fuse information in RNNs is the sum. In this work, we use a RNN extended type, Long Short-Term Memory (LSTM) and we use it for image classification, to which we give a sequential interpretation. Since the data used may not be independent to each other, we modify the sum operator of an LSTM unit using the n-dimensional Choquet integral, which considers possible data coalitions. We compare our methods to those based on usual aggregation functions, using the datasets Fashion-MNIST and MNIST.
Open Access
Admissible OWA operators for fuzzy numbers
(Elsevier, 2024) García-Zamora, Diego; Cruz, Anderson; Neres, Fernando; Santiago, Regivan; Roldán López de Hierro, Antonio Francisco; Paiva, Rui; Pereira Dimuro, Graçaliz; Martínez López, Luis; Bedregal, Benjamin; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Ordered Weighted Averaging (OWA) operators are some of the most widely used aggregation functions in classic literature, but their application to fuzzy numbers has been limited due to the complexity of defining a total order in fuzzy contexts. However, the recent notion of admissible order for fuzzy numbers provides an effective method to totally order them by refining a given partial order. Therefore, this paper is devoted to defining OWA operators for fuzzy numbers with respect to admissible orders and investigating their properties. Firstly, we define the OWA operators associated with such admissible orders and then we show their main properties. Afterward, an example is presented to illustrate the applicability of these AOWA operators in linguistic decision-making. In this regard, we also develop an admissible order for trapezoidal fuzzy numbers that can be efficiently applied in practice.