Abstract
In this study, we presents the idea of
-intuitionistic fuzzy subgroup (IFSG) defined on
-intuitionistic fuzzy set (IFS). Furthermore, we prove that every IFSG is an
-IFSG. Also, we extend the study of this notion to define
-intuitionistic fuzzy cosets and
-intuitionistic fuzzy normal subgroups of a given group and investigate some of their fundamental algebraic features. Besides, we define the
-intuitionistic fuzzy homomorphism between two
-IFSG's and show that an
-intuitionistic fuzzy homomorphic image (inverse image) of the
-IFSG is an
-IFSG.