A three-way decision model based on cumulative prospect theory

In three-way decision, the description on the risk attitude of decision-makers is a focus topic. In this paper, we propose a novel three-way decision model based on cumulative prospect theory. First, with the aid of a reference point, the value functions are utilized to describe different risk appetites of decision-makers towards gains and losses. Second, the weight functions incorporate the nonlinear transformation of the conditional probability. The cumulative decision weights are decided by taking into account the increasing order of value functions. Then, with value functions and weight functions, the new decision rules of the proposed model are deduced based on the principle of maximizing the cumulative prospect value rather than minimizing the cost. Further, we analyze and prove the existence and uniqueness of thresholds of our model. Then, the decision rules are simplified based on the conditional probability and numerical solutions of thresholds, and the algorithm for deriving three-way decision rules is constructed. Finally, an illustrative example and a series of relevant comparisons are presented to illustrate and validate the effectiveness and feasibility of our model.