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