互反判断矩阵一致性指标研究  

Research into Consistency Indexof Reciprocal Judgement Matrix

作　　者：徐迎军[1] 尹世久[1] 陈默[1] 吴林海 XU Ying-jun;YIN Shi-jiu;CHEN Mo;WU Lin-hai(School of Economics,Qufu Normal University,RiZhao 276826,China;Food Safety Research Base of Jiangsu Province,Jiangnan University,Wuxi 214122,China)

机构地区：[1]曲阜师范大学经济学院,山东日照276826 [2]江南大学江苏省食品安全研究基地,江苏无锡214122

出　　处：《运筹与管理》2020年第3期117-124,共8页Operations Research and Management Science

基　　金：教育部人文社会科学研究青年基金项目(13YJC790169);国家自然科学基金项目(71203122,71371107);江苏省高校人文社科优秀创新团队建设项目(2013CXTD011)。

摘　　要：首先给出了互反判断矩阵与一致性互反判断矩阵集之间距离的定义,基于此定义,提出了一个新的互反判断矩阵一致性指标,并给出了此一致性指标的度量方法。对于不满足此一致性指标的互反判断矩阵,提出了一个迭代算法来提高其一致性程度。得出了群体互反判断矩阵一致性指标的下界,为提出的一致性指标应用于群决策问题提供了理论基础。最后用数值例子说明了该迭代算法的可行性和有效性以及群决策中的相关结论。This paper first proposes the distance definition between a reciprocal judgement matrix and the set of consistent reciprocal judgement matrices,based on which a new consistency index of reciprocal judgement matrix and the measure method of it are proposed,which is the similarity degree between the goal matrix and the consistent matrix constructed based on the goal matrix.For those judgement matrix that don't meet this consistency index,an iterative algorithm is introduced to enhance its consistent degree.One theorem gives the conclusion that the revised judgement matrix which is built after some times of iterations must meet the consistent degree required.In the group decision making section,a theorem gives the conclusion that if several individual judgement matrix all meet the consistent degree demand,then the consistency index of the group judgement matrix constructed based on the individual judgement matrix has a deterministic low limit.Another theorem also proves that if the similarity degree between each individual judgement matrix and the given judgement has one common low limit,then the similarity degree between the group judgement matrix which is constructed based on al the individual judgement matrix and the given judgement matrix has one deterministic low limit.All the conclusions are the basis for the application of the consistency index to group decision making problems.Finally,some examples are given to show the feasibility and efficiency of the algorithm and relevant conclusions in group decision making.

关 键 词：互反判断矩阵 最短距离 一致性指标 迭代算法 

分 类 号：C934[经济管理—管理学]