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中文摘要：
针对多粒度语言判断矩阵的群决策问题提出基于相对熵的最优化模型的排序方法。在多粒度语言偏好信息的导出函数基础上定义了语言判断矩阵对应的导出模糊互补判断矩阵，并给出其排序向量的计算式；同时采用语言判断矩阵的一致性指标来确定专家重要性程度的权向量；在相对熵的意义下构建了群决策排序向量的最优化模型，探讨了模型的求解方法。实例分析表明该模型是可行和有效的。
英文摘要：
In this paper we propose the optimal model based on relative entropy for the group decision making with multi-granularity linguistic judgment matrices. We define fuzzy complementary judgment matrices on the basis of the concept of the corresponding induced functions, and we also give the formula of rank vector. In the meantime, we have used the consistent index to determine the weights of experts in the group decision making. Finally, the optimal model is constructed based on relative entropy for the group decision making with multi-granularity linguistic judgment matrices, and its solution is also discussed. A numerical example shows that the developed approach is feasible and effective.
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