基于前景理论的犹豫模糊TOPSIS多属性决策方法

Hesitant fuzzy TOPSIS multi-attribute decision method based on prospect theory

针对属性权重未知、属性值为犹豫模糊集的决策问题,提出一种前景理论和逼近理想解(TOPSIS)相结合的多属性决策方法.考虑到决策者对指标集的不同偏好,利用犹豫模糊熵的相关理论,提出一种基于犹豫模糊熵的熵权法确定属性权重.将决策者的风险心理因素引入犹豫模糊多属性决策中,定义了犹豫模糊数的前景价值函数,并以此将犹豫模糊决策矩阵转化为价值矩阵,计算出各方案的收益损失比值.最终应用TOPSIS的基本思路,确定备选方案的优劣排序,并通过算例分析验证了所提出方法的有效性.

A decision method of integrating the prospect theory with TOPSIS is proposed for multi-attribute decision- making, where the attribute weights are unknown and attribute values are in the form of hesitant fuzzy number. Considering the different attitudes of decision makers toward index sets, An approach to determine the weights of attribute by the entropy method based on the hesitant fuzzy entropy is proposed. The prospect value function of the hesitant fuzzy number is defined by introducing the psychological risk factors of decision makers into hesitant fuzzy multi-attribute decision-making, and the hesitant fuzzy decision-making matrix is converted to the value matrix based on which the ratio of gains to losses of the alternatives is calculated. Finally, TOPSIS method is used to rank all the alternatives and a numerical example is provided to illustrate the effectiveness of the proposed method.