Miguel Turullols, Laura de

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https://academica-e.unavarra.es/handle/2454/49579

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Miguel Turullols

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Laura de

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Estadística, Informática y Matemáticas

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ISC. Institute of Smart Cities

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0000-0002-7665-2801

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88811

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810922

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Start date: 2020 × Subject: Restricted equivalence functions ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    Extension of restricted equivalence functions and similarity measures for type-2 fuzzy sets
    (IEEE, 2021) Miguel Turullols, Laura de; Santiago, Regivan; Wagner, Christian; Garibaldi, Jonathan M.; Takáč, Zdenko; Roldán López de Hierro, Antonio Francisco; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    In this work we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence functions allow us to compare any two general type-2 fuzzy sets and to generate a similarity measure for type-2 fuzzy sets. The result of this similarity is a fuzzy set on the same referential set (i.e., domain) as the considered type-2 fuzzy set. The latter is crucial for applications such as explainable AI and decision making, as it enables an intuitive interpretation of the similarity within the domain-specific context of the fuzzy sets. We show how this measure can be used to compare type-2 fuzzy sets with different membership functions in such a way that the uncertainty linked to type-2 fuzzy sets is not lost. This is achieved by generating a fuzzy set rather than a single numerical value. Furthermore, we also show how to obtain a numerical value for discrete referential sets.
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    PublicationOpen 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.