一种基于残缺语言判断矩阵的群决策模型

Group decision-making model based on incomplete linguistic judgment matrices

研究了偏好信息为残缺语言判断矩阵的群决策问题。通过创建一个转换公式,将加性语言判断矩阵转化为互补判断矩阵,探讨了判断矩阵转换的一致性;应用转换公式将专家个体的加性残缺语言判断矩阵转化为残缺互补判断矩阵,并利用残缺互补判断矩阵排序向量的和行归一法,求出专家个体的排序向量;根据专家个体的排序向量,通过建立并求解一个非线性规划模型,得到专家群组的排序向量,从而实现备选方案的排序和择优。通过算例说明了方法的可行性与有效性.

This paper discusses group decision-making problem, which preference information is incomplete linguistic judgment matrices. Firstly, by constructing a transformation formula, additive linguistic judgment matrix is transformed into complementary judgment matrix, and a consistency of transformation of judgment matrices is analyzed. Then, additive incomplete linguistic judgment matrix of each expert is transformed into incomplete complementary judgment matrix by using the transformation for- mula, and the priority vector of each expert is obtained by using normalizing rank aggregation method for priority of incomplete complementary judgment matrix. Thirdly, according to the priority vector of each expert, the priority vector of expert group is obtained by building and solving a nonlinear programming model, and the priority of alternatives is determined based on the pri-ority vector of expert group. Finally, an example is used to illustrate the feasibility and applicability of the proposed method.