Characterizations for the cross-migrativity between overlap functions and commutative aggregation functions

Abstract

Previous years, people deeply discussed the cross-migrativity properties of the same binary operators, like two overlap functions. Based on the previous works, we extend the study of the cross-migrativity about two same operators to different operators (i.e., a commutative aggregation function CA and overlap function F). At first, we present a idea respecting cross-migrativity about commutative aggregation functions with overlap operators. Besides, we obtain some equivalent characterizations of CA is cross-migrative over FM and Fw, respectively. Moreover, by the aid of ordinal sum about CA, some related properties on the cross-migrativity equations between CA and FM and F1 are discussed, respectively.