Abstract
In this paper, we define the concept of the support of t-intuitionistic fuzzy set and prove that it forms a normal subgroup of a given group. We establish a relationship about the normality of any two t-intuitionistic fuzzy subgroups of a group. We also initiate the study of t-intuitionistic fuzzy isomorphism between any two t-intuitionistic fuzzy subgroups and prove the fundamental theorems of t-intuitionistic fuzzy isomorphism for these particular fuzzy subgroups.