基于后悔理论的风险型多属性决策方法

Method for risky multiple attribute decision making based on regret theory

在一些现实的风险决策问题中,往往需要考虑决策者的心理行为,而如何将行为决策理论引入到风险决策分析中,这是一个值得关注的研究课题.在考虑决策者行为的情境下,为了解决属性值和状态概率均为区间数的风险型多属性决策问题,提出了一种基于后悔理论的决策分析方法.该方法是基于后悔理论,分别计算关于属性值的效用值和后悔值,然后通过计算效用值和后悔值之和来得到决策者对每个方案的感知效用,进一步地,通过构建方案综合感知效用最大化的优化模型并进行模型的求解来得到方案的排序结果.最后,通过两个算例说明了提出方法的可行性与有效性.

In some practical risky decision making problems, the psychological behavior of the decision maker （DM） should be considered. Thus, how to introduce behavioral decision theory into risky decision analysis deserves more attention. In the situation of considering the DM＇s psychological behavior, a decision analysis method based on regret theory is proposed to solve the risky multiple attribute decision making problem, where attribute values and probabilities of the states are both in the form of interval numbers. Based on regret theory, utility values and regret values concerning attribute values are calculated, respectively. Then, by calculating the sum of utility value and regret value of each alternative, the DM＇s perceived utility value is obtained. Further, by constructing a programming model which satisfies maximum overall perceived utility values of alternatives and solving the model, a ranking of alternatives can be determined. Finally, two numerical examples are used to illustrate the feasibility and validity of the proposed method.