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...
| Autores: | , |
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| 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 |
| 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. |
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