Characterizations for the alpha-cross-migrativity of continuous t-conorms over generated implications

The α-cross-migrativity can be regarded as weaker form of the commuting equation. It has been extensively investigated between some aggregation functions including t-norms, overlap functions, uninorms, and semi-t-operators. Recently, Fang [10] has proposed the α-cross-migrativity of t-conorms over fuzzy implications. This paper continues to consider this research topic and mainly focuses on the fuzzy implications generated by additive (resp. multiplicative) generators of continuous Archimedean t-norms and t-conorms. Full characterizations for the α-cross-migrativity of continuous t-conorms over (f, g)-, k-, h- and (θ, t)-generated implications are obtained. Moreover, some supporting examples for solutions are given.