In this paper we have firstly examined the properties of α and β cuts of intuitionistic fuzzy numbers in R n with the help of well-known Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the generalized Hukuhara difference in intuitionistic fuzzy environment by using the properties of α and β cuts and support function. Finally, we have extended the strongly generalized differentiability concept from fuzzy set theory to intuitionistic fuzzy environment and proved the related theorems with this concept,