Based on intuitionistic uncertain linguistic information, for the decision-making problem of the non-strictly independent and interacting among criteria, the two kinds of the intuitionistic uncertain linguistic Choquet integral operators are proposed. Fristly, the phenomenon of the previous failure intuitionistic uncertain linguistic information aggregation operator handling the interacting criteria is analyzed, the fuzzy measure is introduced, and the intuitionistic uncertain linguistic Choquet weighted averaging operator(IULCWA) and the intuitionistic uncertain linguistic Choquet geometric mean operator(IULCGM) are defined. Then the properties of these operators are proved, and an approach for solving the interacting multiple attribute values taking the form of the intuitionistic uncertain linguistic numbers is considered based on these operators. Finally, an illustrative example is provided to illustrate the limitation of the previous intuitionistic uncertain linguistic information aggregation operator and the effectiveness of the proposed operator.