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Permutable fuzzy consequence and interior operators and their connection with fuzzy relations
Carmona, Neus; Elorza Barbajero, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
Universitat Politècnica de Catalunya. Departament d'Estructures a l'Arquitectura; Universitat Politècnica de Catalunya. FIA - Modelització Matemàtica Funcional i Aplicacions
Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type.; We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh's compositional rule and the inf--> composition. For this cases, we connect permutability of the fuzzy relations (using the sup-* composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
Fuzzy logic
Fuzzy consequence operator
Fuzzy closure operator
Fuzzy interior operator
Fuzzy preorder
Indistinguishability relation
CO-Closure systems
Rough sets
Lògica difusa

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