Studying the multiple criteria decision-making problem where criteria values are interval-valued intuitionistic fuzzy number and the information of criteria weights is incompletely unknown. A bidirectional projection method based on the prospect theory is proposed. Firstly, an interval score function is defined. Secondly, the prospect decision-making matrix is constructed by calculating the prospect value of each alternative, which uses the zero as the reference point. Then, an optimization model, in which the goal of the sum of variance is based on minimizing, is established to obtain the criteria weights via defining the vectors of an alternative and an ideal(critical) alternative. Furthermore, a relative closeness degree formula based on the alternatives is presented in order to rank the alternatives. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.