Abstract: Aiming at the problem that attribute weights are difficult to obtain under the framework of evidential reasoning, a multi-attribute decision method based on improved fuzzy entropy and evidential reasoning was proposed. Firstly, the formula of trigonometric fuzzy entropy under the framework of belief decision matrix of evidential reasoning was defined, and it was proved that it satisfies the four axiomatic definitions of entropy. Secondly, the proposed method can simultaneously deal with two situations in which the attribute weights are completely unknown and the attribute weights information are partially known. When the attribute weights were completely unknown, the attribute weights were calculated based on the basic idea of fuzzy entropy and entropy weight method under the framework of belief. When part of the information of attribute weights were known, the weighted fuzzy entropy was defined, and the linear programming model with the minimum expected fuzzy entropy was established to get the optimal attribute weights. Finally, the evidential reasoning algorithm was used to aggregate the degree of belief of attributes and got the result of the ranking of alternatives combined with expected utility theory. Through example calculations and comparative analysis with the method of traditional fuzzy entropy, it is verified that the proposed method can more fully reflect the original decision information, which is more objective and general.

Key words: Evidential Reasoning (ER), trigonometric fuzzy entropy, objective weight, multiple attribute decision

摘要： 针对证据推理方法框架下属性权重难以获取的问题，提出一种基于改进模糊熵和证据推理的多属性决策方法。首先，定义证据推理信度决策矩阵框架下的三角函数模糊熵公式，并证明了其满足熵的四个公理化定义。其次，所提方法能够同时处理属性权重完全未知和属性权重信息部分已知两种情况：当属性权重完全未知时，基于信度框架下的改进模糊熵和熵权法的基本思想计算属性权重；当属性权重信息部分已知时，定义加权模糊熵，建立期望模糊熵最小的线性规划模型求解最优属性权重。最后，利用证据推理算法融合方案属性值，结合期望效用理论得到方案排序结果。通过实例计算，并与传统模糊熵计算方法进行比较分析，验证了所提方法能够更加充分地反映原始决策信息，更具客观性和一般性。

关键词: 证据推理, 三角模糊熵, 客观权重, 多属性决策