Abstract
In this paper, we propose the concept of \rho anti-intuitionistic fuzzy sets, \rho anti - intuitionistic fuzzy subgroups and prove some of their algebraic properties. We investigate a necessary and sufficient condition for a \rho -anti intuitionistic fuzzy set to be a \rho -anti intuitionistic fuzzy subgroup. We extend this ideology by defining the notions of \rho anti-intuitionistic fuzzy coset, \rho 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 \rho -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_{S_{\rho }} .