Multi-stage group risk decision making with grey numbers based on grey target and prospect theory

Abstract

Purpose – With respect to multi-stage group risk decision-making problems in which all the attribute values take the form of grey number, and the weights of stages and decision makers are unknown, the purpose of this paper is to propose a new decision-making method based on grey target and prospect theory. Design/methodology/approach – First, the sequencing and distance between two grey numbers are introduced. Then, a linear operator with the features of the “rewarding good and punishing bad” is presented based on the grey target given by decision maker, and the prospect value function of each attribute based on the zero reference point is defined. Next, weight models of stages and decision makers are suggested, which are based on restriction of stage fluctuation, the maximum differences of alternatives and the maximum entropy theory. Furthermore, the information of alternatives is aggregated by WA operator, the alternatives are selected by their prospect values. Findings – The comprehensive cumulative prospect values are finally aggregated by WA operator, alternatives are selected or not are judged by the sign of the comprehensive prospect theory, if the prospect value of alternative is negative, the corresponding alternative misses the group decision makers’ grey target, on the contrary, if the prospect value of alternative is positive, the corresponding alternative is dropped into the group decision makers’ grey target, the alternative with positive prospect value whose value is the maximum is selected. Originality/value – Compared with the traditional decision-making methods using expected utility theory which suppose the decision makers are all completely rational, the proposed method is based on irrational which is more in line with the decision maker’s psychology. And this method considers the decision maker’s psychological expectation values about every attribute, different satisfactory grey target about attributes will directly affect decision-making result.