This paper investigates an approach to multiple attribute group decision-making (MAGDM) problems, in which the individual assessments are in the form of triangle interval type-2 fuzzy numbers (TIT2FNs). Firstly, some Frank operation laws of triangle interval type-2 fuzzy set (TIT2FS) are defined. Secondly, some Frank aggregation operators such as the triangle interval type-2 fuzzy Frank weighted averaging (TIT2FFWA) operator and the triangle interval type-2 fuzzy Frank weighted geometric (TIT2FFWG) operator are developed for aggregation TIT2FNs. Furthermore, some desirable properties of the two aggregation operators are analyzed in detail. Finally, an approach based on TIT2FFWA (or TIT2FFWG) operator to solve MAGDM is developed. An illustrative example about supplier selection is provided to illustrate the developed procedures. The results demonstrate the practicality and effectiveness of our new method.