Three-way group decisions based on prospect theory

The three-way decision method is a new developing uncertain decision theory. The method divides a set of decision alternatives into three regions, called the acceptance, rejection, and uncertainty regions constructed from a pair of thresholds. However, seldom researches about three-way decisions take psychological attitudes and preferences of the decision-makers into consideration. In this paper, we propose a novel three-way group decision method, which considers the psychological attitudes from the decision-maker. Firstly, we provide the concept of three-way group decisions. The three-way approximation is constructed by many decision-makers with respect to a single critical value. The objects are still divided into acceptance, rejection, and uncertainty regions, respectively. Then, for the proper region (uncertain region, in general), we propose a decision method, which considers the psychological preferences through fusing prospect theory into three-way group decision methods. The alternatives in the proper region are ranked in accordance with their weighted prospect values. Finally, the optimal choices are made. The decision steps are presented in detail, and the practicality of the proposed methods is illustrated through an example.