Complex-Valued Migrativity of Complex Fuzzy Operations

Abstract

Complex fuzzy sets (CFSs), as an important extension of fuzzy sets, have been investigated in the literature. Operators of CFSs are of high importance. In addition, $\alpha -$ migrativity for various fuzzy operations on [0, 1] has been well discussed, where $\alpha$ is a real number and $\alpha \in \left[\mathrm{0,1}\right]$ . Thus, this paper studies $\alpha -$ migrativity for binary functions on the unit circle of the complex plane $\mathbf{O}$ , where $\alpha$ is a complex number and $\alpha \in \mathbf{O}$ . In particular, we show that a binary function is $\alpha -$ migrativity for all $\alpha \in \mathbf{O}$ if and only if it is $\alpha -$ migrativity for all $\alpha \in \left[\mathrm{0,1}\right]\cup \overline{\mathbf{O}}$ , where $\overline{\mathbf{O}}$ is the boundary point subset of $\mathbf{O}$ . Finally, we discuss the relationship between migrativity and rotational invariance of binary operators on $\mathbf{O}$ .