基于相对熵的残缺语言判断矩阵群排序方法

针对残缺语言判断矩阵的群决策问题，提出一种基于相对熵的群排序方法。首先，定义一种用于识别残缺语言判断矩阵可接受的残缺度指标；其次，将残缺语言型偏好转化成残缺数值型偏好，根据相对熵与加性一致性算法，构建决策者对方案排序向量的最优模型；再次，通过构建接近度熵权与相似度熵权指标，对决策者权重进行动态调整，得到稳定的决策者权重，进而得出群体排序向量；最后，通过应用算例进行验证，以表明所提出的方法是可行的。

Group ranking based on relative entropy with incomplete linguistic judgment matrices

With respect to group decision making problems (GDM) with preference relations in form of incomplete linguistic judgment matrices, a group ranking method is proposed based on the relative entropy. Firstly, an incomplete degree is defined which is used to distinguish the degree of acceptance with incomplete linguistic judgment matrices. Secondly, the incomplete linguistic preference is transformed into incomplete numerical preference by using the transformation formula, and an optimize model for alternative ranking vectors is constructed according to the theory of relative entropy and additive consistency. Thirdly, a proximity entropy and similarity entropy indicator is defined, and decision makers’ weights are adjusted dynamically according to the two indicators until the steady weights of decision makers are obtained, so that the final group ranking vectors are calculated. Finally, numerical examples are illustrated to verify the effectiveness of the proposed method.