Similarity in fuzzy reasoning

Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indist...

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Detalles Bibliográficos
Autores: Klawonn, Frank, Castro Peña, Juan Luis
Tipo de recurso: artículo
Fecha de publicación:1995
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2099/2472
Acceso en línea:https://hdl.handle.net/2099/2472
Access Level:acceso abierto
Palabra clave:Fuzzy sets
Conjunts borrosos
Lògica difusa
Classificació AMS::03 Mathematical logic and foundations::03E Set theory
Descripción
Sumario:Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval as the basis for fuzzy sets, to the framework of GL--monoids that can be understood as a generalization of MV--algebras. Residuation is a basic concept in GL--monoids and many proofs can be formulated in a simple and clear way instead of using special properties of the unit interval.