Abstract:

Considering the Multi-Attribute Decision Making（MADM） problem in Pythagorean hesitant fuzzy environment, a Pythagorean hesitant fuzzy grey correlation MADM method based on the prospect theory is proposed. The grey correlation degree and prospect value degree of Pythagorean hesitant fuzzy number are presented. Based on the grey correlation degree, the difference sets of each alternative with respect to the positive and negative ideal solutions are defined, and Pythagorean hesitant fuzzy decision matrix are transformed into value matrix by combining the prospect value function. The alternatives are ranked by the ratio of gains to losses. To illustrate the feasibility and effectiveness of the decision-making method, the proposed method is applied to the comprehensive evaluation of energy projects, and the superiority of the proposed decision method is verified by an example.

Key words: Pythagorean hesitant fuzzy number, prospect theory, grey correlation degree, multi-attribute decision making

摘要：

针对Pythagorean犹豫模糊环境下的多属性决策问题，提出了一种基于前景理论的Pythagorean犹豫模糊灰色关联多属性决策方法。定义了Pythagorean犹豫模糊数的灰色关联度和前景价值函数。基于灰色关联度定义了各方案相对于正负理想解的差异集，结合前景价值函数将Pythagorean犹豫模糊决策矩阵转化为价值矩阵。通过各方案的收益损失比值对备选方案进行优劣排序。为了说明该决策方法的可行性和有效性，将其应用到能源项目的综合评价上，并通过实例对比验证了提出决策方法的优越性。

关键词: Pythagorean犹豫模糊数, 前景理论, 灰色关联度, 多属性决策