Migrativity properties of uninorms over 2-uninorms

Abstract

In the field of fuzzy set theory, whether from the perspective of theory or practical application, as an important property, the migrativity has an extraordinary significance for the research of binary aggregation functions. There have been a lot of contributions on migrativity properties for some binary aggregation functions, for instance, t-norms, t-operators, uninorms, mayor's operators, copulas and so on, but few for 2-uninorms. Therefore, we make a deep study on the migrativity of uninorms over 2-uninorms in this article. According to whether the absorbing element of a 2-uninorm is consistent with the neutral element of a uninorm or not, we study the migrativity properties of uninorms in the usual classes over the three different subclasses of 2-uninorms. In addition, all solutions of the migrative equations are respectively analyzed and characterized for all possible combinations of uninorms in the usual classes and the three different subclasses of 2-uninorms. The usual classes of uninorms consist of Umine1, Umaxe1, Urepe1, Uidee1, Ucos,mine1 and Ucos,maxe1, while the three different subclasses of 2-uninorms are made up of C0, C1 and Ck.