Open Access
Extensions of fuzzy sets in image processing: an overview
(EUSFLAT, 2011) Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Galar Idoate, Mikel; Jurío Munárriz, Aránzazu; López Molina, Carlos; Paternain Dallo, Daniel; Sanz Delgado, José Antonio; Couto, Pedro; Melo-Pinto, Pedro; Automática y Computación; Automatika eta Konputazioa
This work presents a valuable review for the interested reader of the recent Works using extensions of fuzzy sets in image processing. The chapter is divided as follows: first we recall the basics of the extensions of fuzzy sets, i.e. Type 2 fuzzy sets, interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets. In sequent sections we review the methods proposed for noise removal (sections 3), image enhancement (section 4), edge detection (section 5) and segmentation (section 6). There exist other image segmentation tasks such as video de-interlacing, stereo matching or object representation that are not described in this work.
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
Hyperspectrum comparison using similarity measures
(IEEE, 2017-08-31) López Molina, Carlos; Marco Detchart, Cedric; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; López Maestresalas, Ainara; Ayala Martini, Daniela; Automática y Computación; Automatika eta Konputazioa; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta Proiektuak
Similarity measures, as studied in the context of fuzzy set theory, have been proven applicable to many different fields. Surely, their primary role is to model the perceived (dis-) similarity between two fuzzy sets or, equivalently, the linguistic terms they represent. However, the richness of the dedicated study makes the similarity measures portable to other contexts in which quantitative comparison plays a key role. In this work we present the application of similarity measures to hyperspectrum comparison in the context of in-lab hyperspectral imaging for bioengineering.
Open Access
From restricted equivalence functions on Ln to similarity measures between fuzzy multisets
(IEEE, 2023) Ferrero Jaurrieta, Mikel; Takáč, Zdenko; Rodríguez Martínez, Iosu; Marco Detchart, Cedric; Bernardini, Ángela; Fernández Fernández, Francisco Javier; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from L to L n and present a new similarity construction on L n . Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.
Open Access
Do we still need fuzzy classifiers for small data in the era of big data?
(IEEE, 2019) Elkano Ilintxeta, Mikel; Bustince Sola, Humberto; Galar Idoate, Mikel; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13
The Era of Big Data has forced researchers to explore new distributed solutions for building fuzzy classifiers, which often introduce approximation errors or make strong assumptions to reduce computational and memory requirements. As a result, Big Data classifiers might be expected to be inferior to those designed for standard classification tasks (Small Data) in terms of accuracy and model complexity. To our knowledge, however, there is no empirical evidence to confirm such a conjecture yet. Here, we investigate the extent to which state-of-the-art fuzzy classifiers for Big Data sacrifice performance in favor of scalability. To this end, we carry out an empirical study that compares these classifiers with some of the best performing algorithms for Small Data. Assuming the latter were generally designed for maximizing performance without considering scalability issues, the results of this study provide some intuition around the tradeoff between performance and scalability achieved by current Big Data solutions. Our findings show that, although slightly inferior, Big Data classifiers are gradually catching up with state-of-the-art classifiers for Small data, suggesting that a unified learning algorithm for Big and Small Data might be possible.
Open Access
Strong negations and restricted equivalence functions revisited: an analytical and topological approach
(Elsevier, 2021) Bustince Sola, Humberto; Campión Arrastia, María Jesús; Miguel Turullols, Laura de; Induráin Eraso, Esteban; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Throughout this paper, our main idea is to analyze the concepts of a strong negation and a restricted equivalence function, that appear in a natural way when dealing with theory and applications of fuzzy sets and fuzzy logic. Here we will use an analytical and topological approach, showing how to construct them in an easy way. In particular, we will also analyze some classical functional equation related to those key concepts.
Open Access
Admissible orders on fuzzy numbers
(IEEE, 2022) Zumelzu, Nicolás; Bedregal, Benjamin; Mansilla, Edmundo; Bustince Sola, Humberto; Díaz, Roberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this paper, we introduce the notion of admissible order for fuzzy numbers equipped with a partial order, i.e. a total order which refines the partial order. In particular, it is given special attention to the partial order proposed by Klir and Yuan in 1995. Moreover, we propose a method to construct admissible orders on fuzzy numbers in terms of linear orders defined for intervals considering a strictly increasing upper dense sequence, proving that this order is admissible for a given partial order. Finally, we use admissible orders to ranking the path costs in fuzzy weighted graphs. IEEE