Algebraic Characteristics of Anti-Intuitionistic Fuzzy Subgroups Over a Certain Averaging Operator

In this paper, we propose the concept of ρ anti-intuitionistic fuzzy sets, ρ anti - intuitionistic fuzzy subgroups and prove some of their algebraic properties. We investigate a necessary and sufficient condition for a ρ-anti intuitionistic fuzzy set to be a ρ-anti intuitionistic fuzzy subgroup. We extend this ideology by defining the notions of ρ anti-intuitionistic fuzzy coset, ρ anti-intuitionistic fuzzy normal subgroup and derive some of their key algebraic characteristics. In addition, we study the quotient group of a group induced by ρ-anti intuitionistic fuzzy normal subgroup and establish a group isomorphism between this newly defined quotient group and the quotient group of group G relative to its particular normal subgroup G
_Sρ
.