Based on the definition of admissible order for interval-valued Atanassov intuitionistic fuzzy sets, we study ordered weighted averaging operators in these sets, distinguishing between the weights associated with the membership and those associated with the nonmembership degree, which may differ from the latter. We also study Choquet integrals for aggregating information, which is represented using interval-valued Atanassov intuitionistic fuzzy sets. We conclude with two algorithms to choose the best alternative in a decision-making problem when we use this kind of sets to represent information.