Based on the fundamental notions of intuitionistic fuzzy sets, and in consideration of the effects of the three factors-the membership, the non-membership and the probability distribution, two extensions of intuitionistic fuzzy sets, i.e. statistical intuitionistic fuzzy sets and multi-value intuitionistic fuzzy sets, are presented. The calculations and relations of extending the intuitionistic fuzzy sets are introduced. Thus, the intuitionistic fuzzy sets are further extended and applied.