Migrativity properties of uninorms over fuzzy implications

Abstract

Migrativity between fuzzy logical connectives is an important and interesting property in fuzzy logic theory. So far, the migrativity between conjunctive logic connectives including t-norms, uninorms and overlap functions has been extensively studied. Recently, we [23] studied the migrativity of continuous t-conorms over fuzzy implications, which is a theoretical supplement on the migrativity of disjunctive connectives in the literature. It is well known that uninorms are a special kind of aggregation functions, which can be viewed as generalizations of both t-norms and t-conorms, and within this framework, we carry out a continuous deep investigation on the migrativity of uninorms over fuzzy implications in this paper. We first introduce the concept of alpha-migrativity of uninorms over fuzzy implications and then characterize the migrative equation for the uninorms U belonging to one of the usually-studied classes over fuzzy implications whose natural negation is non-vanishing. Finally, we study the \(\alpha \)-migrativity of uninorms over general fuzzy implications and obtain the characterizations of solutions to migrative equations by the ordinal sum of t-conorms (t-norms), where plenty of supporting examples of solutions are given.