The Algebraic Structures of Complex Intuitionistic Fuzzy Soft Sets Associated with Groups and Subgroups

Abstract

In recent years, the theory of complex fuzzy sets has captured the attention of many researchers, and research in this area has intensified in the past five years. However, almost all of the researchers in this area have focused on the development of various complex fuzzy based models as well as constructing decision making processes using current decision making approaches and tools. In this spirit, this paper focuses on developing the algebraic structures pertaining to groups and subgroups for the complex intuitionistic fuzzy soft set model. This paper was constructed based on the complex intuitionistic fuzzy soft set model which is characterized by a membership and a non-membership structure for both the amplitude and phase terms of the elements. This model was chosen due to its dual-membership structure that is better able to handle the uncertainties and partial ignorance that exists in most complex data, whilst retaining all the characteristics and advantages of complex fuzzy sets. Besides examining the properties and structural characteristics of the algebraic structures, the relationship between the algebraic structures introduced here and the corresponding algebraic structures in fuzzy group theory and classical group theory were also discussed and verified.