The purpose of this paper is to commence studying the incompatibility in the Atanassov's intuitionistic fuzzy sets framework. In order to do this, firstly we deal with the concept of T -incompatible sets, where T is an intuitionistic t- norm, relating it with the N-contradictory sets, where N is a intuitionistic fuzzy negation. Next, an axiomatic model for measuring T -incompatibility is introduced, and finally some methods for obtaining families of such measures are provided