Based on the interval intuitionistic linguistic variables and the Frank operator, the operational laws of the Frank operator under the interval intuitionistic linguistic circumstance are firstly defined. Then, several interval intuitionistic linguistic Frank aggregation operators are introduced, such as the interval intuitionistic linguistic Frank weighted average operator, the interval intuitionistic linguistic Frank weighted geometric operator, and the interval intuitionistic linguistic Frank generalized weighted average operator, etc. and some of their properties are discussed. Moreover, two approaches are introduced on the basis of the interval intuitionistic linguistic Frank aggregation operators, and an example is given to illustrate the feasibility and effectiveness of the proposed approaches.