关键词: 群决策, 残缺语言判断矩阵, 残缺互补判断矩阵, 非线性规划模型

Abstract: 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 formula, 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 priority vector of expert group. Finally, an example is used to illustrate the feasibility and applicability of the proposed method.

Key words: group decision making, incomplete linguistic judgment matrix, incomplete complementary judgment matrix, nonlinear programming model