A prospect theory-based three-way decision model

Abstract

In three-way decision, how to reflect the risk attitude in determining decision rules is an important issue. In the classical three-way decision model, loss functions are used to measure risks and determine the minimum-cost decision rules. On this basis, the utility function has been used as a new risk measurement to determine the maximum-utility decision rules. However, some studies show that utility theory may produce some paradoxes and cannot reflect the real risk attitude. To address this problem, we propose a prospect theory-based three-way decision model. In this scenario, we use prospect theory to describe decision-makers’ risk attitudes and utilize the value function as a new risk measurement. The decision rules are induced based on the principle of prospect value maximization. Then, we analyze and prove the existence and uniqueness of thresholds. Two specific analytic solutions of thresholds are calculated and the simplified decision rules are derived. A case study is presented to illustrate the effectiveness of our model and make comparisons with other related models. Finally, the results of the experimental analysis are reported to validate the feasibility and performance of our proposed model.