加权幂平均复合判断矩阵的群体AHP一致性研究  

Research on the Consistency and Consensus of Group AHP with Weighted Power Mean Co mplex Judge ment Matrix

作　　者：周金明 苏为华[2] 朱晓临[3] ZHOU Jin-ming;SU Wei-hua;ZHU Xiao-lin(School of Mathematics and Physics,Anhui Polytechnic University,Wuhu,241000,China;School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou,310018,China;School of Mathematics,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]安徽工程大学数理学院,安徽芜湖241000 [2]浙江工商大学统计与数学学院,浙江杭州310018 [3]合肥工业大学数学学院,安徽合肥230009

出　　处：《运筹与管理》2020年第4期158-164,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(71671165);安徽省高等学校人文社会科学研究重点项目(SK2019A0116);安徽省高等教育提升计划自然科学研究项目(TSKJ2017B22)。

摘　　要：判断矩阵一致性是群体综合评价的重要内容。一致性可以反映专家群体就所有可能的替代方案达成完全一致的意见,利用一致性测度可以衡量评价者之间的差异,也是共识判断的基础。文章针对加权幂平均复合判断矩阵中存在的一致性问题进行研究,从幂平均次数对复合判断矩阵影响的角度,分析幂平均次数对一致性比率的影响程度,揭示两者之间的变化规律;研究专家判断矩阵的阶数对一致性比率的作用;从群体专家权重的角度,研究权重对复合判断矩阵一致性比率的敏感性。结果表明:(1)幂平均的次数会影响复合判断矩阵的一致性,幂平均的次数在有限区间内保证复合判断矩阵的满意一致性,有限区间长度同时依赖于判断矩阵的阶数与幂平均的次数,且一致性比率是关于幂平均次数的凹函数;(2)判断矩阵的阶数越高,专家给出判断矩阵的难度加大,然而随着判断矩阵阶数的升高,一致性比率会呈递减趋势;(3)专家的权数对于一致性比率影响较小,即专家权数的灵敏度较低,给定权数的扰动后不会影响复合判断矩阵的满意一致性。In the view of the complex judgment matrix effects with the degree of power mean,the influence degree of the degree to consistency ratio is studied.The order of the matrix on the consistency ratio is also developed.From the perspective of group expert weight,the sensitivity of weight to the consistency ratio of complex judgment matrix is proposed.The examples show that;(1)the power mean will affect the consistency of the complex judgment matrix,and the consistency ratio is concave function of the power average number.(2)the higher the order number of the judgment matrix,the more difficult it is to judge the matrix;but the higher the order number of the judgment matrix,the consistency ratio will decrease.(3)the influence of experts on the consistency ratio is little,that is,the sensitivity of the expert weight is low,and the satisfaction consistency of the compound judgment matrix will not be affected by the perturbation of the given weights.

关 键 词：幂平均 复合判断矩阵 一致性 

分 类 号：C934[经济管理—管理学]