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研究了方案判断矩阵为不同粒度语言判断矩阵和专家权重为语言标度的群决策问题.通过拓展相关文献中建立的转换函数的使用范围,将专家给出的不同粒度语言判断矩阵转化为互补判断矩阵,并证明了转化的合理性,同时,将专家语言权重向量转化为数值单位权重向量.然后,利用积型一致性互补性判断矩阵和互补判断矩阵的排序向量之间的偏差,建立一个非线性规划模型,求出互补判断矩阵的排序向量,根据合成矩阵的排序向量实现方案的排序择优.最后,通过一个实例来说明方法的可行性与有效性.
This paper studies the problem that the program judgment matrix is a group decision making problem with different granularity linguistic judgment matrices and expert weights as linguistic scales.Through expanding the scope of application of the transfer functions established in the relevant literatures, the linguistic judgment matrices given by experts are transformed into complementary judgment Matrix, and prove the rationality of the transformation, at the same time, the expert language weight vector is transformed into the weight vector of the numerical unit.And then, by using the product type consistency complementary complementarity judgment matrix and the complementary judgment matrix, Linear programming model to find the ranking vectors of complementary judgment matrix, and to optimize the ranking of the schemes according to the ranking vector of the synthetic matrix.Finally, an example is given to illustrate the feasibility and effectiveness of the method.