CONTRAPOSITIVE SYMMETRY OF FUZZY IMPLICATIONS

Contrapositive symmetry of R- and QL-implications defined from t-norms , t-conorms and strong negations is studied. For R-implications, chara cterizations of contrapositive symmetry are proved when the underlying t-norm satisfies a residuation condition. Contrapositive symmetrizati on of R-implications not having this property makes it possible to def ine a conjunction so that the residuation principle is preserved. Case s when this associated conjunction is a t-norm are characterized. As a consequence, a new family of t-norms (called nilpotent minimum) owing several attractive properties is discovered. Concerning QL-implicatio ns, contrapositive symmetry is characterized by solving a functional e quation. When the underlying t-conorm is continuous and the t-norm is Archimedean, the t-conorm must be isomorphic to the Lukasiewicz one, w hile the t-norm must be isomorphic to a member from the well-known Fra nk family of t-norms. Finally, contrapositive symmetry for some new fa milies of fuzzy implications is investigated.