Non-conventional conjunctions and implications in fuzzy logic

Abstract

First, we make some remarks concerning the definition of connectives in fuzzy logic. We point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for the conjunction and disjunction. Coincidence of S- and It-implications is investigated by solving functional equations for conjunctions. Then, we suggest a constructive approach to axiomatics of the generalized modus ponens (GMP). Besides a special model, a particular class of conjunctions satisfying the axioms for GMP and based on the Hamacher family of t-norms is also characterized. On the other hand, the coincidence of R- and S-implications defined by the members of this class is verified.