A Novel Concept of Complex Anti-Fuzzy Isomorphism over Groups

Abstract

In this research article, the fundamental properties of complex anti-fuzzy subgroups as well as the influence of group homomorphisms on their characteristics are investigated. Both the necessary and sufficient conditions for a complex anti-fuzzy subgroup are defined; additionally, the image, inverse image and some vital primary features of complex anti-fuzzy subgroups are examined. Moreover, the homomorphic and isomorphic relations of complex anti-fuzzy subgroups under group homomorphism are discussed, and numerical examples for various scenarios to describe complex anti-fuzzy symmetric groups are provided. Finally, it is proven that every homomorphic image of a complex anti-fuzzy cyclic group is cyclic, but the converse may not be true.