The migrativity equation for uninorms revisited

The migrativity equation with interesting applications in decision making and image processing has been extensively discussed involving different kinds of aggregation functions from t-norms and t-conorms to uninorms, nullnorms and some generalizations of them. In recent papers, the already known results concerning the migrativity of two uninorms are based on the assumption that both uninorms belong to one of the most studied classes of uninorms. In this paper we will explore the migrativity equation involving uninorms in a most general setting. Specifically, we will study the migrativity between two uninorms in the cases when the second uninorm lies in any of the most studied classes of uninorms, but the first one is any uninorm with no further assumptions. We will show along the paper that many new solutions appear from this new point of view that were not included in the previous approaches.