On the migrativity of uninorms and nullnorms over overlap and grouping functions

In this paper, we investigate the migrativity of uninorms and nullnorms over any fixed overlap function or grouping function. First, we introduce the concept of (α,O)-migrative uninorms over any fixed overlap function O. In addition, we show equivalent characterizations of the (α,O)-migrativity equation when the uninorm U belongs to one certain class (e.g. Umin, Umax, the family of idempotent uninorms, representable uninorms or uninorms continuous on ]0,1[2). And then, we give the notion of (α,G)-migrative uninorms over any fixed grouping function G and propose the (α,G)-migrativity equation using an analogous method. Finally, we discuss the (α,O)-migrative and (α,G)-migrative nullnorms and obtain equivalent characterizations of the related (α,O)-migrativity and (α,G)-migrativity equations, respectively.