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dc.contributor.authorKlawonn, Frank
dc.contributor.authorCastro Peña, Juan Luis
dc.description.abstractFuzzy 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.
dc.publisherUniversitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
dc.relation.ispartofMathware & soft computing . 1995 Vol. 2 Núm. 3
dc.rightsReconeixement-NoComercial-CompartirIgual 3.0 Espanya
dc.subject.otherFuzzy sets
dc.titleSimilarity in fuzzy reasoning
dc.subject.lemacConjunts borrosos
dc.subject.lemacLògica difusa
dc.subject.amsClassificació AMS::03 Mathematical logic and foundations::03E Set theory
dc.rights.accessOpen Access
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Salvo que se indique lo contrario, los contenidos de esta obra estan sujetos a la licencia de Creative Commons: Reconocimiento-NoComercial-SinObraDerivada 3.0 España