Bipolar Complex Fuzzy Subgroups

Abstract

In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) set, bipolar complex characteristic function, and BCF point. Then, we interpret the BCF subgroup, BCF normal subgroup, BCF conjugate, normalizer for BCF subgroup, cosets, BCF abelian subgroup, and BCF factor group. Furthermore, we present the associated examples and theorems, and prove these associated theorems. After that, we interpret the image and pre-image of BCF subgroups under homomorphism and prove the related theorems.