The proliferation of extensions of intuitionistic fuzzy sets makes it difficult to compare properties between different models for decision making. We shall approach this topic in the framework of interval valued intuitionistic fuzzy sets. In this respect, the aim of this work is twofold. At a theoretical level, we prove two theorems that transform interval valued intuitionistic fuzzy sets into suitably related pairs of intuitionistic fuzzy sets. On a more practical level, we show how these results can be utilized for aggregating interval valued intuitionistic fuzzy sets, and applied to group decision making in this framework.