On fuzzy implication operators.

*(English)*Zbl 0736.03006Summary: 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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\textit{J. C. Fodor}, Fuzzy Sets Syst. 42, No. 3, 293--300 (1991; Zbl 0736.03006)

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