Properties of the probabilistic implications and S-implications

Michał Baczyński , Przemysław Grzegorzewski , Piotr Helbin , Wanda Niemyska

Abstract

implications and probabilistic S-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In his previous papers author gave a motivation to his idea and indicates some interesting connections between new families of implications and the dependence structure of the underlying environment. In this paper the laws of contraposition, the law of importation and T-conditionality are studied for these families of fuzzy implications. Furthermore, we discuss the intersections of both new families of implications with R-implications, SN-implications and QL-operations.