Migrativity Properties Of Uninorms Over 2-uninorms

In the field of fuzzy set theory,whether from the perspective of theory or practical application,as an important property,the migrativity has an extraor-dinary significance for the research of binary aggregation functions.There have been a lot of contributions on migrativity properties for some binary aggrega-tion functions,for instance t-norms,t-operators,uninorms,mayor’s operators,copulas and so on,but few for 2-uninorms.Moreover,2-uninorms generalizes uninorms and nullnorms.A characterization for migrativity of uninorms over 2-uninorms is meaningful not only in their applications in fuzzy quantifiers or net-works but also helps scholars to characterize the general structure of 2-uninorms,since they have three different subclasses,which are strongly linked to other op-erators.Therefore,we make a deep study on the migrativity of uninorms over 2-uninorms in this article.Starting from whether the absorbing element of a 2-uninorm is consistent with the neutral element of a uninorm or not,we s-tudy the migrativity properties of uninorms in the usual classes over the three different subclasses of 2-uninorms,in addition,all solutions of the migrativity functional 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.