基于前景理论的犹豫二元语义灰关联群决策法

针对偏好信息为犹豫二元语义形式、专家权重和属性权重均完全未知的多属性群决策问题，基于前景理论和灰色关联分析法的思想，提出一种多属性群决策方法.首先，利用矩阵拉直运算和灰色关联分析法确定专家权重，利用偏差最大化法确定属性权重.其次，给出了两个犹豫二元语义元的比较方法，结合该比较方法确定各决策矩阵的正、负理想方案，并以此作为决策参考点.然后，根据前景理论和灰色关联系数确定犹豫二元语义环境下的前景价值函数，进而确定各方案的收益损失比值，并据此对候选方案进行排序.最后，将所提方法应用于一个投资决策算例，其结果表明了该方法的合理性和有效性.

Hesitant 2-Tuple Linguistic Grey Relational Group Decision-Making Approach Based on Prospect Theory

For the multi-attribute group decision-making problems, where the information of the attribute weights and the expert weights is completely unknown and the preference information is in the form of hesitant 2-tuple linguistic, a multi-attribute group decision-making method based on the prospect theory and the grey relation analysis is proposed. Firstly, the weights of the experts are determined by the matrix vec operator and the grey relation analysis, and the weights of attributes are calculated by the maximizing deviation method. Subsequently, a comparison method of the hesitant 2-tuple linguistic elements is given, and the positive and negative ideal solutions based on that are determined and used as the decision reference point. Then the hesitant 2-tuple linguistic prospect value function according to the prospect theory and the grey relational coefficient is acquired, and then the ratio of the gains to losses of the alternatives is obtained, and the alternatives are ranked accordingly. Finally, the proposed method is applied to a numerical example of investment decision, and the results show the rationality and effectiveness of the method.