Some Characterizations of Certain Complex Fuzzy Subgroups

Abstract

The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (ρ,η)-complex fuzzy sets, (ρ,η)-complex fuzzy subgroupoid, (ρ,η)-complex fuzzy subgroups and describe important examples of the symmetric group under (ρ,η)-complex fuzzy sets. Additionally, we discuss the conjugacy class of the group with respect to (ρ,η)-complex fuzzy normal subgroups. We define (ρ,η)-complex fuzzy cosets and elaborate upon the certain operation of this analog to group theoretic operation. We prove that factors regarding the (ρ,η)-complex fuzzy normal subgroup form a group and establish an ordinary homomorphism. Moreover, we create the (ρ,η)-complex fuzzy subgroup of the factor group.