基于前景理论的不确定TOPSIS多属性决策方法

针对属性权重未知、属性值为犹豫模糊集的多属性决策问题，本文提出一种基于前景理论和粗糙集的多属性决策方法，充分考虑了决策者心理风险因素对决策结果的影响.首先，以正、负理想点作为参考点计算各属性下的前景价值函数，定义新的综合前景值，并根据给定的阈值得到判断矩阵；然后，根据判断矩阵进行属性约简，确定属性权重；最后，计算各备选方案的加权综合前景值，利用TOPSIS方法对备选方案进行排序，并通过算例证实该方法的可行性和有效性.

Prospect Theory-Based TOPSIS Method for Multiple Attribute Decision Making with Uncertainty

For the multi-attribute decision making problem with attribute weights being unknown and attribute values being hesitant fuzzy sets, this study proposes a multi-attribute decision making method based on prospect theory and rough set, which fully considers the influence of decision makers'' psychological risk factors on decision results. Firstly, the positive and negative ideal points are used as reference points to calculate the prospect value function under each attribute and to define a new comprehensive prospect value, and a discernibility matrix is obtained according to the given threshold. Then, according to the discernibility matrix, attribute reduction is performed to determine the attribute weight. Finally, the weighted comprehensive prospect value of each alternative is calculated, and the TOPSIS method is used to rank all the alternatives. An example is given to illustrate the feasibility and effectiveness of the proposed method.