Abstract
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.
Highlights
In Mathematics, group theory is one of the most important part of algebra
The rest of the paper is organized as follow: Section 2 contains some basic definitions of complex intuitionistic fuzzy sets (CIFSs) and intuitionistic fuzzy subgroups (IFSGs) and a related result which plays a significant role in our further discussion
In this article, we have defined the notion of π -IFSG, CIFSG, level subset and intersection of CIFS
Summary
In Mathematics, group theory is one of the most important part of algebra. Group theory has an effective framework to analyze an object that appears in symmetric form. The study of complex intuitionistic fuzzy subgroups is very important algebraic structure like intuitionistic fuzzy subgroups and intuitionistic fuzzy subrings. The phase term in the complex intuitionistic fuzzy sets can be used to precisely epitomize the cycles appear in intuitionistic fuzzy algebraic structures. The aspiration to draw this unique proficiency of the phase term existence in the complex intuitionistic fuzzy model in the study of fuzzy algebra served as the main motivation to commence and establish the theory of complex intuitionistic fuzzy subgroups in this article. The rest of the paper is organized as follow: Section 2 contains some basic definitions of complex intuitionistic fuzzy sets (CIFSs) and intuitionistic fuzzy subgroups (IFSGs) and a related result which plays a significant role in our further discussion. We show that direct product of CIFSGs is CIFSG
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