Similarity in fuzzy reasoning
- Klawonn, Frank
- Castro Peña, Juan Luis
ISSN: 1134-5632
Année de publication: 1995
Volumen: 2
Número: 3
Pages: 197-228
Type: Article
D'autres publications dans: Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology
Résumé
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.