Abstract: Complex intuitionistic fuzzy sets (CIFS) can represent human information that contains uncertainty and periodicity semantics concurrently. In this research, the generalization concepts of CIF-subgroup (CIFSG) and anti-CIFSG of a given group are introduced, and their significance lies in assigning the grade of membership and non-membership functions in the complex plane. Also, CIFSG and anti-CIFSG are an inspiring expansion of the intuitionistic fuzzy subgroup (IFSG) and anti-IFSG. Our modification is highlighted in the phase term for membership and non-membership functions. Subsequently, a numerical example illustrates the inherent conditions of CIFSG is given. Also, we prove the relation between the complement of CIFSG and anti-CIFSG. After applying the operations ◇, and ▢ to a CIFSG, the results are CIFSG. Also, the intersection of two CIFSGs is as well a CIFSG. Moreover, the complex normal intuitionistic fuzzy subgroup (CNIFSG) and its algebraic properties are presented and investigated. Some equivalent conditions to show that a CIFSG is CNIFSG are obtained.

Keywords: Fuzzy sets, Intuitionistic fuzzy set, Complex Intuitionistic fuzzy set, complex fuzzy subgroup, complex intuitionistic fuzzy subgroup, anti-complex intuitionistic fuzzy subgroup, and complex normal intuitionistic fuzzy subgroup

Pages: 346-358