Considering the importance of the hesitation degree, a multiple criteria fuzzy decision making method based on interval-valued intuitionistic fuzzy number is proposed for the situations where the information about criteria weights is completely unknown. The vectors of an alternative, and an ideal(critical) alternative are defined. A bidirectional projection measure method is proposed, in which the criteria values are in the form of the interval-valued intuitionistic fuzzy set. An
optimization model is established to obtain the criteria weights. A relative closeness degree formula based on the alternatives is presented in order to rank the alternatives. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.