Person:
Fernández Castillo, Jesús

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First Name
Jesús
Last Name
Fernández Castillo
URI
https://hdl.handle.net/20.500.14352/76208
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Químicas
Department
Química Física
Area
Química Física
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2010 - 20164
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Author: Pagola, M. × Has files: true ×

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Now showing 1 - 4 of 4
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    A historical account of types of fuzzy sets and their relationships
    (IEEE Transactions on Fuzzy Systems, 2016) Bustince, H.; Barrenechea, Edurne; Fernández Castillo, Jesús; Pagola, M.; Xu, Z.; Bedregal, B.; Montero, Javier; Hagras, H.; Herrera, F.; De Baets, B.
    In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.
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    Contrast of a fuzzy relation.
    (Information Sciences, 2010) Bustince, H.; Barrenechea, E.; Fernández Castillo, Jesús; Pagola, M.; Montero, Javier; Guerra, C.
    In this paper we address a key problem in many fields: how a structured data set can be analyzed in order to take into account the neighborhood of each individual datum. We propose representing the dataset as a fuzzy relation, associating a membership degree with each element of the relation. We then introduce the concept of interval-contrast, a means of aggregating information contained in the immediate neighborhood of each element of the fuzzy relation. The interval-contrast measures the range of membership degrees present in each neighborhood. We use interval-contrasts to define the necessary properties of a contrast measure, construct several different local contrast and total contrast measures that satisfy these properties, and compare our expressions to other definitions of contrast appearing in the literature. Our theoretical results can be applied to several different fields. In an Appendix A, we apply our contrast expressions to photographic images.
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    Generation of Interval-Valued Fuzzy Negations from Trillas’ Theorem. The Case of Interval Type-2 Fuzzy Sets
    (Enric Trillas: A Passion for Fuzzy Sets. A Collection of Recent Works on Fuzzy Logic, 2015) Bustince, H.; Barrenechea, E.; Fernández Castillo, Jesús; Pagola, M.; Montero, Javier; Magdalena, Luis; Verdegay, José Luis; Esteva, Francesc
    In this work we introduce a method for building interval-valued negations using the characterization theorem for strong negations which was proposed by Trillas in 1979. We also show that interval type-2 fuzzy sets are a three dimensional representation of interval-valued fuzzy sets and we analyze the problems to build complementation for such interval type-2 fuzzy sets. We finally propose a method to construct this complementation.
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    Paired structures in knowledge representation.
    (Knowledge-Based Systems, 2016) Montero, Javier; Bustince, H.; Franco, C.; Rodríguez, Juan Tinguaro; Gómez, Daniel; Pagola, M.; Fernández Castillo, Jesús; Barrenechea, E.
    In this position paper we propose a consistent and unifying view to all those basic knowledge representation models that are based on the existence of two somehow opposite fuzzy concepts. A number of these basic models can be found in fuzzy logic and multi-valued logic literature. Here it is claimed that it is the semantic relationship between two paired concepts what determines the emergence of different types of neutrality, namely indeterminacy, ambivalence and conflict, widely used under different frameworks (possibly under different names). It will be shown the potential relevance of paired structures, generated from two paired concepts together with their associated neutrality, all of them to be modeled as fuzzy sets. In this way, paired structures can be viewed as a standard basic model from which different models arise. This unifying view should therefore allow a deeper analysis of the relationships between several existing knowledge representation formalisms, providing a basis from which more expressive models can be later developed.