An improved three-way decision model based on prospect theory

In three-way decision, how to describe the risk attitudes of decision-makers is an important issue. The prospect theory is widely used to reflect decision-makers' risk attitudes and the decision rules are based on the maximum prospect value. However, the previous three-way decision models based on prospect theory neglected time outcome or they included time outcome in monetary outcome in decision process. In fact, in some cases, time outcome is a more important element in decision making, and without considering it directly may weaken the rationality of decision results. To address these problems, we construct an improved three-way decision model based on prospect theory, which simultaneously and directly considers time outcome and monetary outcome. Specially, this model is a multi-objective optimization model. Firstly, prospect theory is used to describe decision-makers' risk attitudes toward monetary gains and losses as well as time gains and losses. Secondly, we construct a multi-objective optimization model and introduce preference coefficients to transform it into a single objective optimization model, which is based on the maximum comprehensive prospect value. Further, the existence and uniqueness of thresholds are proven, and the decision rules are given. Finally, an illustrative example and some comparative analyses are presented, which validate the rationality and superiority of our improved model.