Abstract: In this paper, we investigate the multi-attribute group decision making problems with binding conditions of attribute weight information and unknown attribute weights in the framework of interval-valued intuitionistic fuzzy set (IVIFS). Firstly, a collective interval-valued intuitionistic fuzzy (IVIF) decision making matrix is determined by integrating all the decision making matrices derived from every decision makers. Secondly, we obtain the distance degree values between every alternative and the ideal-positive alternative depending on the technique for order preference by similarity to an ideal solution (TOPSIS) method. Finally, the ranking order of all the alternatives is determined through the obtained distance degree values. On one hand, a linear-programming method based on an accuracy function of IVIFS is proposed to calculate the attribute weights aiming at the decision making problem with binding attribute weight conditions. On the other hand, we propose a new definition of IVIF entropy, and choose attribute weights according to the information quantity of every alternative depending on IVIF entropy aiming at the decision making problem with completely unknown attribute weight information. The simulation shows the validity and feasibility of the proposed decision making methods.