A Prospect Theory Based Approach to Multiple Attribute Decision Making Considering the Decision Maker’s Attitudinal Character

The decision maker’s attitudinal character towards risk and the psychological aspects are critical factors of the multiple attribute decision making (MADM) problems. In this paper, we consider the attitudinal character during the whole decision making procedure. The reference points associated with prospect theory are in the form of interval-valued intuitionistic fuzzy number (IVIFN) and we assume the membership degree and non-membership degree of the IVIFN obey normal distribution according to the central limit theorem. We combine the properties of normal distribution and the attitudinal character associated with the ordered weighted averaging (OWA) operator to convert all the reference points into crisp numbers. We construct one feasible multiple objective optimization programming to obtain the optimal weight vector of the attributes by minimizing the deviation between the alternative and the reference point corresponding to each alternative. The hybrid weighted averaging (HWA) operator is applied to aggregate the prospect values for each alternative. Especially, we directly reorder the weighted prospect values considering their plus or minus, which reflects the decision-maker’s attitudinal character towards risk as well. Finally, an illustrative example about group-buying is provided to show the feasibility of the proposed method.