Open Access
Pseudo overlap functions, fuzzy implications and pseudo grouping functions with applications
(MDPI, 2022) Zhang, Xiaohong; Liang, Rong; Bustince Sola, Humberto; Bedregal, Benjamin; Fernández Fernández, Francisco Javier; Li, Mengyuan; Ou, Qiqi; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability.
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
Gated local adaptive binarization using supervised learning
(CEUR Workshop Proceedings (CEUR-WS.org), 2021) Fumanal Idocin, Javier; Uriarte Barragán, Juan; Osa Hernández, Borja de la; Bardozzo, Francesco; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Image thresholding is one of the most popular problems in image processing. However, changes inlightning and contrast in an image can cause trouble for the existing algorithms that use a global threshold for all the image. A solution for this problem is the adaptive thresholding, in which an image canhave different thresholds for different parts of the image. Yet, the problem of choosing the most suitable threshold for each region of the image is still open. In this paper we present the Gated Local Adaptive Binarization algorithm, in which we choose the most appropriate threshold for each region of the image using a logistic regression. Our results show that this algorithm can effectively learn the most appropriate threshold in each situation, and beats other adaptive binarization solutions for a standard dataset in the literature.
Open Access
Application of two different methods for extending lattice-valued restricted equivalence functions used for constructing similarity measures on L-fuzzy sets
(Elsevier, 2018) Palmeira, Eduardo S.; Bedregal, Benjamin; Bustince Sola, Humberto; Paternain Dallo, Daniel; Miguel Turullols, Laura de; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Based on previous investigations, we have proposed two different methods to extend lattice-valued fuzzy connectives (t-norms, t-conorms, negations and implications) and other related operators, considering a generalized notion of sublattices. Taking into account the results obtained and seeking to analyze the behavior of both extension methods in face of fuzzy operators related to image processing, we have applied these methods so as to extend restricted equivalence functions, restricted dissimilarity functions and Ee,N-normal functions. We also generalize the concepts of similarity measure, distance measure and entropy measure for L-fuzzy sets constructing them via restricted equivalence functions, restricted dissimilarity functions and Ee,N-normal functions

Bustince Sola, Humberto

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