On the migrativity properties between uni-nullnorms and overlap (grouping) functions

Based on the concepts of the α-migrativity between overlap (grouping) functions and uninorms (nullnorms), in this paper, we introduce and study the α-migrativity between a uni-nullnorm V and a given overlap (grouping) function. First of all, we propose the notion of the (α,O)-migrative uni-nullnorms over a given overlap function O. And then, we explore some equivalent characterizations of the (α,O)-migrativity equation when the uni-nullnorm V pertains to one of the common types. Besides, we consider the concept of (α,G)-migrative uni-nullnorms over a given grouping function G and study the (α,G)-migrativity equation using analogous methods. Moreover, we propose the concept of (α,V)-migrative overlap (grouping) functions over a given uni-nullnorm V and explore the necessary and sufficient conditions of the (α,V)-migrativity equation solutions if the uni-nullnorm V pertains to one certain class.