A method for risky multiple attribute decision making considering regret and rejoicing of the decision maker

In practical risky multiple attribute decision making (RMADM) problems, the decision maker (DM) usually considers the anticipated regret and rejoicing in the decision process. This is the potential psychological behavior of the DM, that can influence the decision result, but it has not received extensive attention from existing RMADM methods. The purpose of this paper is to develop a method for solving RMADM problems by considering the regret and rejoicing of the DM. In this paper, the outcomes of alternatives concerning attributes are in three different formats (crisp numbers, fuzzy numbers and random variables), which are unified into the format of random variables with cumulative distribution functions. Then, by measuring the superior and inferior values in the comparison of the two cumulative distribution functions, the regret and rejoicing values in the pairwise comparisons of alternatives are calculated. Furthermore, according to regret theory, the utility for each alternative is calculated, which considers the regret and rejoicing effects of all the other alternatives. Based on the utility values, a ranking of alternatives is determined. Finally, an illustrative example of the selection of a new product development project is given, and a comparison analysis between our proposed method and the existing methods is presented to verify the validity and feasibility of the proposed method.