Abstract
In this study, the t -intuitionistic fuzzy normalizer and centralizer of t intuitionistic fuzzy subgroup are proposed. The t -intuitionistic fuzzy centralizer is normal subgroup of t -intuitionistic fuzzy normalizer and investigate various algebraic properties of this phenomena. We also introduce the concept of t -intuitionistic fuzzy Abelian and cyclic subgroups and prove that every t -intuitionistic fuzzy subgroup of Abelian (cyclic) group is t -intuitionistic fuzzy Abelian (cyclic) subgroup. We show that the image and pre-image of t -intuitionistic fuzzy Abelian (cyclic) subgroup are t -intuitionistic fuzzy Abelian (cyclic) subgroup under group homomorphism.