This paper provides an approach based on the modified prospect theory solving the intuitionistic fuzzy stochastic multi-criteria decision-making problem where the information of criteria weights is partially known. Firstly, a new score function is defined, by which the intuitionistic fuzzy numbers can be transformed into the real numbers. Then, considering that decision-makers are not completely rational and there are differences among them, the types of decision-makers attitudes towards risk can be classified into risk-seeking, risk-neutral and risk-averse. The modified prospect value decision-making matrix is constructed by applying the modified prospect theory and adjusting its parameters to fit different types of decision-makers. In addition, a nonlinear quadratic deviation optimization model is established, whose goal is maximizing the total difference of criteria values and at the same time minimizing the difference between criteria weights. Furthermore, the order of alternatives is listed on the basis of the integrated utility values, which are derived by the modified prospect decision-making matrix and criteria weights. Finally, an example is given to illustrate the effectiveness and rationality of the proposed method.