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On fuzzy implication operators. (English) Zbl 0736.03006
Summary: There exist several constructions for fuzzy implication operators via conjunctions. In this paper we present a unifying approach to the generation of implications and we prove that for a rather general class of conjunctions the generation process is closed. In addition, all well- known families of fuzzy implications are within our framework. The results support that the class of weak t-norms having the exchange property seems to be a good model of the conjunction (or equivalently, of intersection) operator in fuzzy set theory.

MSC:
03B52 Fuzzy logic; logic of vagueness
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