Abstract: Considering the impact on the multi-criteria decision from risk attitudes, in view of the multi-criteria decision problem with interval numbers, a method based on prospect theory is proposed. The “rewarding good and punishing bad” [[-1,1]] linear transformation operator is used to standardize the original decision-making information and get the positive and negative bull’s eye. According to the prospect theory and grey target decision-making method, the prospect value function is defined, and the comprehensive prospect values are calculated. A decision tree is constructed to determine the optimal program with the maximum prospect value. An investment decision-making model validates the feasibility and effectiveness of the model.

Key words: risk decision-making, prospect theory, grey target theory, decision tree

摘要： 考虑决策者风险态度对多指标决策的影响，针对决策信息为区间数的多指标风险型决策问题，提出一种基于前景理论的灰色多指标风险型决策方法。首先利用“奖优罚劣”的[[-1,?1]]线性变换算子对指标为区间数的原始信息进行规范化处理，得到正负靶心。根据前景理论和灰靶理论定义区间数的价值函数和概率权重函数，并以此求解方案的综合前景值，构造决策树并根据前景值最大化思想进行剪枝确定最优方案。通过一个投资实例说明了该模型的有效性和可行性。

关键词: 风险型决策, 前景理论, 灰靶理论, 决策树