Open Access
A method for inference in approximate reasoning based on normal intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Burillo López, Pedro; Mohedano Salillas, Victoria; Automática y Computación; Automatika eta Konputazioa
This paper introduces a method of approximate inference which operates with nornal intuitionistic fuzzy. We give a definition of degree of compatibility between intuitionistic fuzzy sets and we present a method for the construction of these sets. Lastly we present the method of inference in approximate reasoning with normal intuitionistic fuzzy sets and we study its most immediate properties.
Embargo
Non-symmetric over-time pooling using pseudo-grouping functions for convolutional neural networks
(Elsevier, 2024-07-01) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Miguel Turullols, Laura de; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Convolutional Neural Networks (CNNs) are a family of networks that have become state-of-the-art in several fields of artificial intelligence due to their ability to extract spatial features. In the context of natural language processing, they can be used to build text classification models based on textual features between words. These networks fuse local features to generate global features in their over-time pooling layers. These layers have been traditionally built using the maximum function or other symmetric functions such as the arithmetic mean. It is important to note that the order of input local features is significant (i.e. the symmetry is not an inherent characteristic of the model). While this characteristic is appropriate for image-oriented CNNs, where symmetry might make the network robust to image rigid transformations, it seems counter-productive for text processing, where the order of the words is certainly important. Our proposal is, hence, to use non-symmetric pooling operators to replace the maximum or average functions. Specifically, we propose to perform over-time pooling using pseudo-grouping functions, a family of non-symmetric aggregation operators that generalize the maximum function. We present a construction method for pseudo-grouping functions and apply different examples of this family to over-time pooling layers in text-oriented CNNs. Our proposal is tested on seven different models and six different datasets in the context of engineering applications, e.g. text classification. The results show an overall improvement of the models when using non-symmetric pseudo-grouping functions over the traditional pooling function.
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
Uso de t-normas para el estudio de la convexidad en conjuntos difusos intervalo-valuados
(Universidad de Málaga, 2021) Huidobro, Pedro; Alonso, Pedro; Bustince Sola, Humberto; Janis, Vladimír; Montes Rodríguez, Susana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En muchos problemas reales no se pueden tomar medidas de forma exacta. Así, los conjuntos difusos surgieron como una forma de intentar tratar con la incertidumbre de la forma más eficiente posible. Por otro lado, debe señalarse que la ‘convexidad es un concepto interesante en varias áreas dentro de las matemáticas. Teniendo esto en cuenta, en este documento proponemos una extensión del concepto de convexidad para conjuntos difusos intervalo-valuados basada en el uso de t-normas para intervalos. Para ello, y teniendo en consideración la literatura científica existente respecto de t-normas, presentamos una definición de t-norma aplicada a intervalos. Por último, comprobamos que nuestra definición de convexidad, utilizando t-normas, preserva la convexidad a través de intersecciones, es decir, que la intersección de dos conjuntos difusos intervalo-valuados convexos es también convexa.
Open Access
On admissible orders on the set of discrete fuzzy numbers for application in decision making problems
(MDPI, 2021) Riera, Juan Vicente; Massanet, Sebastia; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The study of orders is a constantly evolving topic, not only for its interest from a theoretical point of view, but also for its possible applications. Recently, one of the hot lines of research has been the construction of admissible orders in different frameworks. Following this direction, this paper presents a new representation theorem in the field of discrete fuzzy numbers that enables the construction of two families of admissible orders in the set of discrete fuzzy numbers whose support is a closed interval of a finite chain, leading to the first admissible orders introduced in this framework.
Open Access
Fuzzy clustering to encode contextual information in artistic image classification
(Springer, 2022) Fumanal Idocin, Javier; Takáč, Zdenko; Horanská, Lubomíra; Bustince Sola, Humberto; Cordón, Óscar; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Automatic art analysis comprises of utilizing diverse processing methods to classify and categorize works of art. When working with this kind of pictures, we have to take under consideration different considerations compared to classical picture handling, since works of art alter definitely depending on the creator, the scene delineated or their aesthetic fashion. This extra data improves the visual signals gotten from the images and can lead to better performance. However, this information needs to be modeled and embed alongside the visual features of the image. This is often performed utilizing deep learning models, but they are expensive to train. In this paper we utilize the Fuzzy C-Means algorithm to create a embedding strategy based on fuzzy memberships to extract relevant information from the clusters present in the contextual information. We extend an existing state-of-the-art art classification system utilizing this strategy to get a new version that presents similar results without training additional deep learning models.
Open Access
Some preference involved aggregation models for basic uncertain information using uncertainty transformation
(IOS Press, 2020) Yang, RouJian; Jin, LeSheng; Paternain Dallo, Daniel; Yager, Ronald R.; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In decision making, very often the data collected are with different extents of uncertainty. The recently introduced concept, Basic Uncertain Information (BUI), serves as one ideal information representation to well model involved uncertainties with different extents. This study discusses some methods of BUI aggregation by proposing some uncertainty transformations for them. Based on some previously obtained results, we at first define Iowa operator with poset valued input vector and inducing vector. The work then defines the concept of uncertain system, on which we can further introduce the multi-layer uncertainty transformation for BUI. Subsequently, we formally introduce MUT-Iowa aggregation procedure, which has good potential to more and wider application areas. A numerical example is also offered along with some simple usage of it in decision making.
Open Access
CFM-BD: a distributed rule induction algorithm for building compact fuzzy models in Big Data classification problems
(IEEE, 2020) Elkano Ilintxeta, Mikel; Sanz Delgado, José Antonio; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Galar Idoate, Mikel; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Interpretability has always been a major concern for fuzzy rule-based classifiers. The usage of human-readable models allows them to explain the reasoning behind their predictions and decisions. However, when it comes to Big Data classification problems, fuzzy rule based classifiers have not been able to maintain the good tradeoff between accuracy and interpretability that has characterized these techniques in non-Big-Data environments. The most accurate methods build models composed of a large number of rules and fuzzy sets that are too complex, while those approaches focusing on interpretability do not provide state-of-the-art discrimination capabilities. In this paper, we propose a new distributed learning algorithm named CFM-BD to construct accurate and compact fuzzy rule-based classification systems for Big Data. This method has been specifically designed from scratch for Big Data problems and does not adapt or extend any existing algorithm. The proposed learning process consists of three stages: Preprocessing based on the probability integral transform theorem; rule induction inspired by CHI-BD and Apriori algorithms; and rule selection by means of a global evolutionary optimization. We conducted a complete empirical study to test the performance of our approach in terms of accuracy, complexity, and runtime. The results obtained were compared and contrasted with four state-of-the-art fuzzy classifiers for Big Data (FBDT, FMDT, Chi-Spark-RS, and CHI-BD). According to this study, CFM-BD is able to provide competitive discrimination capabilities using significantly simpler models composed of a few rules of less than three antecedents, employing five linguistic labels for all variables.
Open Access
Reduction of complexity using generators of pseudo-overlap and pseudo-grouping functions
(2024) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Zhang, Xiaohong; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Overlap and grouping functions can be used to measure events in which we must consider either the maximum or the minimum lack of knowledge. The commutativity of overlap and grouping functions can be dropped out to introduce the notions of pseudo-overlap and pseudo-grouping functions, respectively. These functions can be applied in problems where distinct orders of their arguments yield different values, i.e., in non-symmetric contexts. Intending to reduce the complexity of pseudo-overlap and pseudo-grouping functions, we propose new construction methods for these functions from generalized concepts of additive and multiplicative generators. We investigate the isomorphism between these families of functions. Finally, we apply these functions in an illustrative problem using them in a time series prediction combined model using the IOWA operator to evidence that using these generators and functions implies better performance.
Open Access
A survey of fingerprint classification Part I: taxonomies on feature extraction methods and learning models
(Elsevier, 2015) Galar Idoate, Mikel; Derrac, Joaquín; Peralta, Daniel; Triguero, Isaac; Paternain Dallo, Daniel; López Molina, Carlos; García, Salvador; Benítez, José Manuel; Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
This paper reviews the fingerprint classification literature looking at the problem from a double perspective. We first deal with feature extraction methods, including the different models considered for singular point detection and for orientation map extraction. Then, we focus on the different learning models considered to build the classifiers used to label new fingerprints. Taxonomies and classifications for the feature extraction, singular point detection, orientation extraction and learning methods are presented. A critical view of the existing literature have led us to present a discussion on the existing methods and their drawbacks such as difficulty in their reimplementation, lack of details or major differences in their evaluations procedures. On this account, an experimental analysis of the most relevant methods is carried out in the second part of this paper, and a new method based on their combination is presented.