Open Access
A supervised fuzzy measure learning algorithm for combining classifiers
(Elsevier, 2023) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Fuzzy measure-based aggregations allow taking interactions among coalitions of the input sources into account. Their main drawback when applying them in real-world problems, such as combining classifier ensembles, is how to define the fuzzy measure that governs the aggregation and specifies the interactions. However, their usage for combining classifiers has shown its advantage. The learning of the fuzzy measure can be done either in a supervised or unsupervised manner. This paper focuses on supervised approaches. Existing supervised approaches are designed to minimize the mean squared error cost function, even for classification problems. We propose a new fuzzy measure learning algorithm for combining classifiers that can optimize any cost function. To do so, advancements from deep learning frameworks are considered such as automatic gradient computation. Therefore, a gradient-based method is presented together with three new update policies that are required to preserve the monotonicity constraints of the fuzzy measures. The usefulness of the proposal and the optimization of cross-entropy cost are shown in an extensive experimental study with 58 datasets corresponding to both binary and multi-class classification problems. In this framework, the proposed method is compared with other state-of-the-art methods for fuzzy measure learning.
Open Access
Additively generated (a,b)-implication functions*
(IEEE, 2023) Santos, Helida; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Paiva, Rui; Lucca, Giancarlo; Moura, Bruno; Cruz, Anderson; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Some problems involving classification through neural networks are known to use inputs out of the scope of the unit interval. Therefore, defining operations on arbitrary closed real intervals may be an interesting strategy to tackle this issue and enhance those application environments. In this paper we follow the ideas already discussed in the literature regarding (a,b)-fusion functions, and (a,b)-negations, to provide a new way to construct implication functions. The main idea is to construct an operator using additively generated functions that preserve the properties required by implication functions.
Open Access
On generalized overlap and grouping indices in n-dimensional contexts
(Springer, 2025-05-08) Asmus, Tiago da Cruz; Dimuro, Graçaliz Pereira; Lucca, Giancarlo; Marco Detchart, Cedric; Santos, Helida; Camargo, Heloisa A.; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Overlap and grouping indices are functions measuring, respectively, the fuzzy intersection and fuzzy union of two fuzzy sets. They have been applied successfully in several fields, such as in interpolative fuzzy systems, fuzzy rule-based classification systems and comparison of fuzzy inference rules. Overlap and grouping indices can be built employing overlap and grouping functions, respectively, which are possibly non-associative aggregation functions with features that provide good results when applied to practical bivariate problems. Many studies have generalized the concepts of overlap and grouping functions to be applied in n-dimensional problems. However, the concepts of overlap/grouping indices have not been generalized in similar pattern. Since the associative property may not hold, their application in n-dimensional domains, for comparing more than two fuzzy sets at a time, is not immediate, which limit their application in such contexts. The objective of this paper is to introduce the concepts of n-dimensional and general overlap/grouping indices, with special attention to the development of their construction methods based on generalized overlap/grouping functions. As an application example, we introduce the concept of n-dimensional Jaccard index, with a construction method based on n-dimensional overlap/grouping indices, providing an n-dimensional fuzzy set similarity score.
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.
Embargo
Representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions
(Elsevier, 2025-03-01) Wang, Yiding; Qiao, Junsheng; Zhang, Wei; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
At present, (quasi-)overlap functions have been extended to various universes of discourse and become a hot research topic. Meanwhile, the investigation of extended aggregation operations for normal convex fuzzy truth values has also attracted much attention. This paper mainly studies the representation of quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions, which is the fundamental problem in the whole study of overlap functions for normal convex fuzzy truth values. Firstly, we present the definitions of (restrictive-)quasi-overlap functions and lattice-ordered-(restrictive-)quasi-overlap functions for normal convex fuzzy truth values and generalized extended overlap functions, respectively. Secondly, we present the (equivalent) characterizations for the closure properties of generalized extended overlap functions for various fuzzy truth values. Thirdly, we characterize the basic properties of generalized extended overlap functions for normal convex fuzzy truth values. Finally, by an equivalent characterization with a prerequisite, we successfully represent quasi-overlap functions for normal convex fuzzy truth values based on generalized extended overlap functions. Notably, we can quickly obtain (restrictive-)quasi-overlap functions for normal convex fuzzy truth values using the left-continuous quasi-overlap functions on interval [0,1]. Moreover, regarding the relationships between four types of quasi-overlap functions for normal convex fuzzy truth values, the details implication relations are that lattice-ordered-(restrictive-)quasi-overlap functions are strictly stronger than (restrictive-)quasi-overlap functions for normal convex fuzzy truth values even if all of them are constructed by generalized extended overlap functions.
Open Access
Probabilistic study of induced ordered linear fusion operators for time series forecasting
(Elsevier, 2024) Baz, Juan; Ferrero Jaurrieta, Mikel; Díaz, Irene; Montes Rodríguez, Susana; Beliakov, Gleb; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The aggregation of several predictors in time series forecasting has been used intensely in the last decade in order to construct a better resulting model. Some of the most used alternatives are the ones related to the Induced Ordered Weighted Averaging (IOWA), in which the prediction values are ordered using a secondary vector, often related to the accuracy of the prediction model in the last prediction. Although the time series study has been historically a subject related to statistics and stochastic processes, the random behaviour of the aggregation process is typically not considered. In addition, extensions of aggregation functions with a weaker notion of monotonicity, pre-aggregation functions, are appearing as better alternative for some topics such us classification. In this paper, a pre-aggregation extension of the IOWA operator, the Induced Ordered Linear Fusion (IOLF), is defined as a way to aggregate time series model predictions and its behaviour is studied from a probabilistic point of view. The IOLF operator over random vectors is defined, its properties studied and the relation between some averaging aggregation functions established. The expressions of the optimal weights according to statistical criteria are derived. The advantages and consequences of the use of the IOLF operator are studied, and its behaviour is compared to the usual procedures. Numerical results illustrate its performance on a practical example.
Open Access
Fuzzy integrals for edge detection
(Springer, 2023) Marco Detchart, Cedric; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; López Molina, Carlos; Borges, Eduardo N.; Rincón Arango, Jaime Andrés; Julian, Vicente; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this work, we compare different families of fuzzy integrals in the context of feature aggregation for edge detection. We analyze the behaviour of the Sugeno and Choquet integral and some of its generalizations. In addition, we study the influence of the fuzzy measure over the extracted image features. For testing purposes, we follow the Bezdek Breakdown Structure for edge detection and compare the different fuzzy integrals with some classical feature aggregation methods in the literature. The results of these experiments are analyzed and discussed in detail, providing insights into the strengths and weaknesses of each approach. The overall conclusion is that the configuration of the fuzzy measure does have a paramount effect on the results by the Sugeno integral, but also that satisfactory results can be obtained by sensibly tuning such parameter. The obtained results provide valuable guidance in choosing the appropriate family of fuzzy integrals and settings for specific applications. Overall, the proposed method shows promising results for edge detection and could be applied to other image-processing tasks.
Open Access
On the stability of fuzzy classifiers to noise induction
(IEEE, 2023-11-09) Fumanal Idocin, Javier; Bustince Sola, Humberto; Andreu-Pérez, Javier; Hagras, Hani; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Tabular data classification is one of the most important research problems in the artificial intelligence. One of the most important desired properties of the ideal classifier is that small changes in its input should not result in dramatic changes in its output. However, this might not be the case for many classifiers used in present day. Fuzzy classifiers should be stronger than their crisp counterparts, as they should be able to handle such changes using fuzzy sets and their membership functions. However, this hypothesis has not been empirically tested. Besides, the concept of 'small change' is somewhat imprecise and has not been quantified yet. In this work we propose to use small and progressively bigger changes in test samples to study how different crisp and fuzzy classifiers behave. We also study how to optimize classifiers to be more resistant to such kind of changes. Our results show that different fuzzy sets have different responses to this problem and have a smoother performance response compared to crisp classifiers. We also studied how to improve this and found that resistance to small changes can also result in a worse overall performance.
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
Systematic review of aggregation functions applied to image edge detection
(MDPI, 2023) Amorim, Miqueias; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Dalmazo, Bruno L.; Marco Detchart, Cedric; Lucca, Giancarlo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of objects. Furthermore, even the definition of an edge is vague as an edge can be considered as the maximum boundary between two regions with different properties. Given the advancement of research in image discontinuity detection, especially using aggregation and pre-aggregation functions, and the lack of systematic literature reviews on this topic, this paper aims to gather and synthesize the current state of the art of this topic. To achieve this, this paper presents a systematic review of the literature, which selected 24 papers filtered from 428 articles found in computer databases in the last seven years. It was possible to synthesize important related information, which was grouped into three approaches: (i) based on both multiple descriptor extraction and data aggregation, (ii) based on both the aggregation of distance functions and fuzzy C-means, and (iii) based on fuzzy theory, namely type-2 fuzzy and neutrosophic sets. As a conclusion, this review provides interesting gaps that can be explored in future work.