A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

• Main Authors: Muhammad Gulzar, M. Haris Mateen, Dilshad Alghazzawi, Nasreen Kausar
• Format: Article
• Language: English
• Published: IEEE 2020-01-01
• Series: IEEE Access
• Subjects: Complex intuitionistic fuzzy set; complex intuitionistic fuzzy subgroup; level subsets; product of complex intuitionistic fuzzy sets; product of complex intuitionistic fuzzy subgroups
• Online Access: https://ieeexplore.ieee.org/document/9244057/

In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and pre-image of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.