基于残缺互补判断矩阵的一种群决策模型

A Group Decision-Making Model Based on Incomplete Complementary Judgment Matrices

研究了基于残缺互补判断矩阵的群决策模型.首先,利用积型残缺一致性互补判断矩阵和互补判断矩阵的排序向量之间的偏差,建立并求解一个非线性规划模型,得到各专家残缺互补判断矩阵的排序向量.然后,通过最小化专家残缺互补判断矩阵的排序向量与专家群组排序向量的偏差,再次建立并求解一个非线性规划模型,得到反映出专家群组偏好的排序向量,从而得到了残缺互补判决矩阵的群决策模型.最后,通过算例说明了方法的可行性。

This paper discusses group decision-making model based on incomplete complementary judgment matrices. Firstly, according to the deviations between the priority vectors of multiplicative consistent incomplete complementary judgment matrices and complementary judgment matrices, the priority vector of incomplete complementary judgment matrix of each expert is obtained by building and solving a nonlinear programming model. Secondly, by minimizing the deviations between priority vectors of incomplete complementary judgment matrix of each expert and complementary judgment matrix of group experts, the priority vectors of group experts is obtained by building and solving a nonlinear programming model. And a group decision-making model based on incomplete complementary judgment matrices is obtained in this paper. Finally, an example is used to illustrate the feasibility and applicability of the proposed method.