Migrativity properties of fuzzy implications over uni-norms

In fuzzy set theory, the migrativity of aggregation functions stands out as a noteworthy subject from both theoretical and practical perspectives. The present paper undertakes a thorough study of the migrativity of fuzzy implications over uni-norms and null-norms. Firstly, leveraging the ordinal sum representations of t-norms and t-conorms, we investigate the migrativity of fuzzy implications over t-norms and t-conorms, which shows some positive results. Further, we characterize the migrative functional equation for fuzzy implications over uni-norms in the usual classes such as uni-norms locally internal on the boundary, uni-norms continuous on the boundary except at their neutral elements, representable uni-norms, idempotent uni-norms, uni-norms continuous in the open unit square, and uni-norms with continuous underlying operators. The results indicate that the structure of the solutions of the migrative functional equation is closely related to the natural negation of fuzzy implications. Finally, we explore the migrativity of fuzzy implications over null-norms.