Eigenvector Method for Ranking Alternatives with Vague Value Measurements  

作　　者：侯福均 吴祈宗 

机构地区：[1]School of Management and Economics,Beijing Institute of Technology

出　　处：《Journal of Beijing Institute of Technology》2009年第2期247-252,共6页北京理工大学学报（英文版）

基　　金：Sponsored by the Basic Research Foundation of Beijing Institute of Technology(BIT-UBF-20070842009)

摘　　要：An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on four assumptions for evaluating alternatives, a ranking eigenvector is defined. And then it is proved, based on positive matrix theory, that the EIM＇s eigenvector corresponding to the maximal eigenvalue is the ranking vector. For alternatives whose characteristics are presented by vague sets, the proposed techniques can evaluate the degree of suitability to which an alternative satisfies the decision-maker＇ s requirement efficiently.An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on four assumptions for evaluating alternatives, a ranking eigenvector is defined. And then it is proved, based on positive matrix theory, that the EIM＇s eigenvector corresponding to the maximal eigenvalue is the ranking vector. For alternatives whose characteristics are presented by vague sets, the proposed techniques can evaluate the degree of suitability to which an alternative satisfies the decision-maker＇ s requirement efficiently.

关 键 词：decision analysis vague set positive matrix EIGENVECTOR alternative ranking 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]