Characterizations for the migrativity of continuous t-conorms over fuzzy implications

Abstract

Migrativity between fuzzy logical connectives is an important property at both sides of theory and practical application in fuzzy logic. The migrativity properties between conjunctive connectives as well as general aggregation functions including t-norms, uninorms, nullnorms and overlap functions have been extensively investigated. Recently, Baczyński et al. (2020) [3] studied the migrativity of fuzzy implications. However, there are no discussions so far on the migrativity between disjunctive connectives and fuzzy implications. The purpose of the present paper is to characterize the migrativity of continuous t-conorms over fuzzy implications, which also provides an answer to Fodor's question on how to define the migrativity of t-conorms. We first describe completely the α-migrativity of continuous t-conorms defined by Baczyński et al. in their latest work, which proves to be the standard dual to the migrativity of t-norms over the product t-norm, but provides a new perspective to study the migrativity of t-conorms. And then, we turn to characterize the migrativity of t-conorms over several specific well-known fuzzy implications, of which some are no longer dual to the migrativity of t-norms, and show some interesting results. Finally, we define α-migrativity of continuous t-conorms over general fuzzy implications and obtain the characterizations of solutions to migrativity equations by the ordinal sum of t-conorms, where some supporting examples for solutions are given.