A method based on the prospect theory is proposed to solve the multiple attribute decision making problem in which single and combination attribute aspirations are provided by the decision-maker. Firstly, according to the prospect theory, the attribute aspirations given by the decision-maker are regarded as the reference points. Then the prospect values of each alternative with regard to all single and combination attribute aspirations are calculated, respectively, and the comprehensive prospect value vector concerning each alternative is constructed. Based on this, the original decision problem is converted into the corresponding generalized prioritized fuzzy constraint satisfaction problem (GPFCSP). Further, the overall satisfaction degree of each alternative with regard to the corresponding reasoning standard is calculated, and the ranking of all alternatives can be determined. Finally, a numerical example is used to illustrate the feasibility of the proposed method.