On alpha-cross-migrativity of t-conorms over fuzzy implications - Fang, Bo Wen (Fuzzy sets and systems, 2023)
As a weaker form of the classical commuting equation, α-cross-migrativity properties between conjunctive connectives including t-norms, uninorms, and overlap functions have been extensively investigated. However, there has been no comparative analysis of the α-cross-migrativity between disjunctive connectives and fuzzy implications. The work is dedicated to the study of α-cross-migrativity involving t-conorms and fuzzy implications. The investigation is presented in two separate parts: the first part focuses on the case that fuzzy implication satisfies some property, especially, the order property. The second one deals with the situation where fuzzy implication belongs to some special classes, i.e., (S,N)-implications, R-implications, and Yager's implications (i.e., f- and g-generated implications). Some interesting results are obtained: full characterizations of α-cross-migrativity for continuous t-conorms over fuzzy implications satisfying the order property, (S,N)-implications, R-implications induced by border continuous t-norms and Yager's implications. As a by-product, some constructions of ordinal sum t-conorms and ordinal sum fuzzy implications satisfying α-cross-migrativity are obtained. Moreover, some supporting examples for solutions are given.