The aim of this article is to study the cut sets of interval valued intuitionistic fuzzy sets. By considering the cut sets of an interval-valued intuitionistic fuzzy set as five valued fuzzy sets, the definitions of four cut sets on interval-valued intuitionistic fuzzy sets are given, which are the generalizations of cuts sets on Zadeh fuzzy sets and the intuitionistic fuzzy sets. It is pointed that the cuts sets of interval-valued intuitionistic fuzzy sets have the same properties as that of the intuitionistic fuzzy sets and Zadeh fuzzy sets. These works provide a powerful tool to study interval-valued intuitionistic fuzzy sets.