Regret Decision-Making Based on Basic Probability Assignment Function

Decision theory based on regret has always been one of the hot spots of decision making. Recently, Yager proposed a new model that combines regret decision with D-S evidence theory for effective decision making. This model has certain rationality and foundation, But the state of nature is obeying the probability distribution rather than the basic probability assignment. Therefore, in this paper, an idea is present to reasonably transform BPA into a probability distribution, and then the expected value of regret is calculated for decision making. According to this idea, a new transferable belief model based on the proportional of elements in the BPA is proposed. A reasonable function is proposed to verify the rationality of the model by combining Deng entropy and evidence distance, and then used to calculate the expected value of regret. As a result, it has a certain guiding value for decision-making.