一种基于群组判断离差的偏好集结方法  

An aggregation approach of preference information according to dispersion of group judgments

作　　者：张仲敏[1,2] 李俊山[1] 宋凭[2] 杨亚威 

机构地区：[1]第二炮兵工程大学信息工程系,西安710025 [2]西安通信学院信息安全系,西安710106

出　　处：《控制与决策》2015年第11期1960-1966,共7页Control and Decision

基　　金：装备维修科学研究与改革项目(2012171)

摘　　要：针对群决策偏好集结中违反Pareto最优性的情况,设计一种基于群组判断几何离差的同质性集结方法.该方法在集结前进行几何离差测试,以确定个体决策信息的离差水平.离差较小时,可基于几何平均集结;对于离差较大且修正复杂度较高的决策信息,采用主成分分析(PCA)从高维决策信息中提取大多数相关信息,在不依赖主观分析的情况下进行加权集结.仿真实验表明,所提出的方法能够在不违背Pareto最优性的基础上集结离差较大的群决策信息.Aiming at the issue of violation of Pareto optimality in the preference aggregation of group decision, a method of homogeneous aggregation based on the geometric dispersion of group judgments is designed. In the method, a dispersion test is carried out to measure the dispersion level of group judgments, and the aggregation is explored based on the dispersion level. For the judgments with the lower dispersion level, it is proposed to combine the judgments with the geometric mean;for the judgments with the higher dispersion level, which are difficult to revise, the principal components analysis（PCA） is applied to capture the majority of the information associated with the original high dimensionality judgments from diversity of opinion, and combine the group judgments according to the weighted geometric mean without subjective analysis. The simulation experiments show that the proposed method can combine the group judgments with the biggish dispersion on the premise of the Pareto optimality principle.

关 键 词：离差 几何平均集结 群组判断 同质性水平 主成分分析 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] E911[自动化与计算机技术—计算机科学与技术]