Axiomatic Considerations of the Concepts of R-Implication and T-Norm

Abstract

In the paper presented we investigate under which conditions there exists a one-to-one correspondance between a class of generalized R-implications and a class of generalized T-norms based on the mutual definability of these classes. Furthermore, we study which properties of functions of the one class will be translated into properties of functions of the other class by the bijection mentioned above. This paper can be considered as a continuation of author s paper dealing with the same problematics for S-implications on the one hand and S-norms (T-conorms) and negations on the other hand.