Migrativity properties of general grouping (overlap) functions with regard to null-norms.

In fuzzy set theory, the migrativity among aggregation functions is a noteworthy topic from both theoretical and applied perspectives, numerous significant findings on the migrative functional equation for various combinations of particular subclasses of aggregation functions have been made in recent decades. Nonetheless, there are very few characterizations on migrativity of null-norms in the existing literature, and it has not been thoroughly studied. The present paper conducts an in-depth study on the migrativity of general grouping functions and general overlap functions with regard to null-norms. Firstly, by means of the ordinal sum representation of t-norms and t-conorms, we characterize the migrativity of general grouping functions with regard to t-norms and t-conorms, which shows some positive results. And then, we describe the structures of the solution of the migrative functional equation for general grouping functions with regard to null-norms. Finally, the migrativity of general overlap functions with regard to null-norms is discussed by duality. [ABSTRACT FROM AUTHOR]