一种基于不同粒度语言判断矩阵的群决策模型

A Group Decision Making Model Based on Multi-granularity Linguistic Judgment Matrices

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.

We study group decision making problem, in which judgment matrices of expert are multi-granularity linguistic judgment matrices and priority vector of expert is linguistic vector. Firstly, by expanding the applied scope of the transformation formula constructed in related reference, linguistic judgment matrix of each expert is transformed into comple- mentary judgment matrix, and rationality of transformation is proven. Meanwhile, linguistic weight vector is transformed into numerical unit weight vector. Then, according to deviation existed between priority vector of multiplicative consistent complementary judgment matrix and complementary judgment matrix, priority vector of complementary judgment matrix is obtained by building and solving a nonlinear programming model. The alternatives are ranked according to priority vector of synthetic matrix. Finally, an example is used to illustrate the feasibility and applicability of the proposed method.