What is a Fuzzy Bi-implication?

• Ano de defesa: 2012
• Autor(a) principal: Olguín, Claudio Andrés Callejas
• Orientador(a): Bedregal, Benjamin René Callejas
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio Grande do Norte
• Programa de Pós-Graduação: Programa de Pós-Graduação em Sistemas e Computação
• Departamento: Ciência da Computação
• País: BR
• Palavras-chave em Português: Bi-implicacão difusa; Equivalência difusa; Di-residuation difusa; Lógica difusa
• Palavras-chave em Inglês: Fuzzy bi-implication; Fuzzy equivalence; Fuzzy bi-residuation; Fuzzy logic
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::SISTEMAS DE COMPUTACAO
• Link de acesso: https://repositorio.ufrn.br/jspui/handle/123456789/18683

In order to make this document self-contained, we first present all the necessary theory as a background. Then we study several definitions that extended the classic bi-implication in to the domain of well stablished fuzzy logics, namely, into the [0; 1] interval. Those approaches of the fuzzy bi-implication can be summarized as follows: two axiomatized definitions, which we proved that represent the same class of functions, four defining standard (two of them proposed by us), which varied by the number of different compound operators and what restrictions they had to satisfy. We proved that those defining standard represent only two classes of functions, having one as a proper subclass of the other, yet being both a subclass of the class represented by the axiomatized definitions. Since those three clases satisfy some contraints that we judge unnecessary, we proposed a new defining standard free of those restrictions and that represents a class of functions that intersects with the class represented by the axiomatized definitions. By this dissertation we are aiming to settle the groundwork for future research on this operator.