A Study of Generalized Fuzzy Dishkant Implications

Abstract

In this paper, we revisit the generalized Dishkant implications and provide analytical proof that they are a new fuzzy implications’ class that contains the known class of Dishkant implications. Both classes are not always fuzzy implications. For this reason we use the term operations instead of implications in general. Nonetheless, it will be demonstrated that a necessary but not sufficient condition for a generalized Dishkant operation to be a fuzzy implication exists. Furthermore, the intersection of the sets of generalized Dishkant operations and Dishkant operations (respectively, implications) is provided. At the end, we prove a theorem for F- conjugation in GDoperations.