AHP中指数标度下的区间数判断矩阵构造及其一致性自动调整方法
摘要
判断矩阵的构造及其一致性调整,是影响AHP法评价结果能否忠实于专家判断意图的关键。为此,文章将专家判断值及对该值的不确定度相结合,构造出基于指数标度下的区间数判断矩阵,并提出与之相适应的一致性自动调整方法。还从理论推导和通过算例验证了该方法的可行性与合理性。最后分析给出了该方法的几点优势。
引文
[1]Saaty T L.The Analytic Hierarchy Process[M].New York:McGraw-Hill,1980.
[2]Belton V.On a Short-coming of Saaty's Method of Analytic Hierarchies[J].Omega,1983,11(3).
[3]Dyer J S.Remarks on the Analytic Hierarchy Process[J].Management Science,1990,36(3).
[4]Barzilai J.Notes on the Analytic Hierarchy Process[C].Proceedings of the NSF Design and Manufacturing Research Conference,2001.
[5]陈伟.正确认识层次分析法(AHP法)[J].人类工效学,2000,6(2).
[6]骆正清,杨善林.层次分析法中几种标度的比较[J].系统工程理论与实践,2004,24(9).
[7]徐泽水,达庆利.3种基于互反判断矩阵的互补判断矩阵排序法[J].东南大学学报(自然科学版),2001,31(5).
[8]瞿浩.基于灰数判断矩阵的Grey-AHP评估方法及其应用研究[J].合肥工业大学学报(自然科学版),2016,39(11).
[9]Azarnivand A.Extended Fuzzy Analytic Hierarchy Process Approach in Water and Environmental Management(Case Study:Lake Urmia Basin,Iran)[J].Environmental Earth Sciences,2015,73(1).
[10]Peláez J I,Lamata M T.A New Measure of Consistency for Positive Reciprocal Matrices[J].Computers&Mathematics With Applications,2003,46(12).
[11]郭亚军,张发明,易平涛.标度选择对综合评价结果的影响及合理性分析[J].系统工程与电子技术,2008,30(7).
[12]吕跃进,张维.指数标度在AHP标度系统中的重要作用[J].系统工程学报,2003,18(5).
[13]刘开第,庞彦军,金斓.浅析模糊AHP中一致性检验的不必要性[J].数学的实践与认识,2015,45(14).
[14]沈继红,付肖燕,赵玉新.感觉判断矩阵的一致性改进[J].哈尔滨工程大学学报,2011,32(3).
[15]Mazurek J.A New Approach to a Derivation of a Priority Vector From an Interval Comparison Matrix in a Group AHP Framework[C].Intelligent Decision Technologies.Switzerland:Springer International Publishing,2016.
[16]Abdullah L,Najib L.A New Preference Scale Mcdm Method Based on Interval-valued Intuitionistic Fuzzy Sets and the Analytic Hierarchy Process[J].Soft Comput,2016,(20).
[17]Abdullah L,Zulkifli N.Integration of Fuzzy AHP and Interval Type-2 fuzzy DEMATEL:An Application to Human Resource Management[J].Exper Systems With Applications,2015,(42).
[18]Dragan S,Pamucar D I.Fuzzification of the Saaty’s Scale and a Presentation of the Hybrid Fuzzy AHP-TOPSIS Model:An Example of the Selection of a Brigade Artillery Group Firing Position in a Defensive Operation[J].Military Technical Courier,2016,64(4).
[19]Saaty T L.A Scaling Method for Priorities in Hierarchical Structures[J].Journal of Mathematical Psychology,1977,(15).
[20]张志勇,刘心报.关于AHP中比率标度的选择问题[A].中国系统工程学会决策科学专业委员会第六届学术年会[C].北京:北京万方数据,2005.
[21]姜艳萍,樊治平,王欣荣.AHP中判断矩阵一致性改进方法的研究[J].东北大学学报(自然科学版),2001,22(4).
[22]叶跃祥.区间数多属性决策的一些问题研究[D].合肥:中国科学技术大学博士论文,2007.
[2]Belton V.On a Short-coming of Saaty's Method of Analytic Hierarchies[J].Omega,1983,11(3).
[3]Dyer J S.Remarks on the Analytic Hierarchy Process[J].Management Science,1990,36(3).
[4]Barzilai J.Notes on the Analytic Hierarchy Process[C].Proceedings of the NSF Design and Manufacturing Research Conference,2001.
[5]陈伟.正确认识层次分析法(AHP法)[J].人类工效学,2000,6(2).
[6]骆正清,杨善林.层次分析法中几种标度的比较[J].系统工程理论与实践,2004,24(9).
[7]徐泽水,达庆利.3种基于互反判断矩阵的互补判断矩阵排序法[J].东南大学学报(自然科学版),2001,31(5).
[8]瞿浩.基于灰数判断矩阵的Grey-AHP评估方法及其应用研究[J].合肥工业大学学报(自然科学版),2016,39(11).
[9]Azarnivand A.Extended Fuzzy Analytic Hierarchy Process Approach in Water and Environmental Management(Case Study:Lake Urmia Basin,Iran)[J].Environmental Earth Sciences,2015,73(1).
[10]Peláez J I,Lamata M T.A New Measure of Consistency for Positive Reciprocal Matrices[J].Computers&Mathematics With Applications,2003,46(12).
[11]郭亚军,张发明,易平涛.标度选择对综合评价结果的影响及合理性分析[J].系统工程与电子技术,2008,30(7).
[12]吕跃进,张维.指数标度在AHP标度系统中的重要作用[J].系统工程学报,2003,18(5).
[13]刘开第,庞彦军,金斓.浅析模糊AHP中一致性检验的不必要性[J].数学的实践与认识,2015,45(14).
[14]沈继红,付肖燕,赵玉新.感觉判断矩阵的一致性改进[J].哈尔滨工程大学学报,2011,32(3).
[15]Mazurek J.A New Approach to a Derivation of a Priority Vector From an Interval Comparison Matrix in a Group AHP Framework[C].Intelligent Decision Technologies.Switzerland:Springer International Publishing,2016.
[16]Abdullah L,Najib L.A New Preference Scale Mcdm Method Based on Interval-valued Intuitionistic Fuzzy Sets and the Analytic Hierarchy Process[J].Soft Comput,2016,(20).
[17]Abdullah L,Zulkifli N.Integration of Fuzzy AHP and Interval Type-2 fuzzy DEMATEL:An Application to Human Resource Management[J].Exper Systems With Applications,2015,(42).
[18]Dragan S,Pamucar D I.Fuzzification of the Saaty’s Scale and a Presentation of the Hybrid Fuzzy AHP-TOPSIS Model:An Example of the Selection of a Brigade Artillery Group Firing Position in a Defensive Operation[J].Military Technical Courier,2016,64(4).
[19]Saaty T L.A Scaling Method for Priorities in Hierarchical Structures[J].Journal of Mathematical Psychology,1977,(15).
[20]张志勇,刘心报.关于AHP中比率标度的选择问题[A].中国系统工程学会决策科学专业委员会第六届学术年会[C].北京:北京万方数据,2005.
[21]姜艳萍,樊治平,王欣荣.AHP中判断矩阵一致性改进方法的研究[J].东北大学学报(自然科学版),2001,22(4).
[22]叶跃祥.区间数多属性决策的一些问题研究[D].合肥:中国科学技术大学博士论文,2007.