Abstract:

This paper introduces the idea of complex numbers to intuitionistic fuzzy sets which enhances the representation of uncertain, hesitant and ambiguous data. By integrating the complex-valued intuitionistic fuzzy membership and non-membership functions with the algebraic structure of multi-polygroups known as Complex Intuitionistic Fuzzy Multi-Polygroups (CIFMPGs). This extension addresses the limitations of classical fuzzy and intuitionistic fuzzy multi-polygroups by introducing both amplitude and phase into the representation of membership values. The basic operations and structural properties were studied such as complement, intersection, containment and cartesian product. Their closure properties on those operations were also established. Furthermore, the concept of Bipolar Complex Intuitionistic Fuzzy Multi-Polygroups (BCIFMPGs) was introduced by integrating the degrees of positive and negative complex-valued membership and non-membership into the multi-polygroups structure. The bipolar extension leads to an algebraic representation of positive and negative information together with amplitude and phase. Basic operations on BCIFMPGs such as intersection and complement were defined, and their closure properties. The introduced structures generalize intuitionistic fuzzy multi-polygroups to complex-valued settings, opening the way for further theoretical study of fuzzy algebraic structures.