基于群决策的AHP判断矩阵的可靠性研究
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摘要
本文认为专家构造判断矩阵的过程应是灰盒子,而不应是黑盒子,专家应给出的是知识矩阵,判断矩阵是知识矩阵中的结论构成的矩阵。本文通过对专家决策过程的模拟,发现判断矩阵的一致性是可靠性的必要条件,但不是充分条件。因此,提出不能以判断矩阵的一致性作为专家意见取舍或评价的唯一标准,而应综合分析专家提供的知识矩阵信息。最终提出确定专家意见可靠性的方法。
专家构造判断矩阵的过程,就是一个不断做出判断的过程。如果一个专家给出的判断矩阵是客观、公正、合理的,则应满足下列条件:
专家有能力,即专家应有相关方面足够的知识和经验。
专家有足够的信息,即专家对各个方案事实有充分的了解。
专家有认真的态度,即不会有非理性的偏好,这一点往往被人们忽视。
对于能力的可靠性,本文通过让专家构造知识矩阵来检验。对于信息(事实)可靠性,本文通过从知识矩阵检验中获得的信息可靠性与最终的判断矩阵做相关分析后给出结论。对专家的态度,本文通过对各方案的误差作方差分析后给出结论。
在完成以上检验后,如果判断矩阵是符合要求的,本文利用遗传算法求得相对稳定的权重向量。
This dissertation agrees on that the process of expert’s making judgment is like a grey box not a black box. The expert should give a knowledge matrix not a judgment matrix only. The dissertation finds that CR value is not a sufficient condition but only an essential condition through imitating expert’s judgment. So value on judgment of expert can’t be available only on CR value. The value should be from knowledge matrix. Finally the dissertation gives a method of evaluating expert’s knowledge matrix.
The process of making judgment matrix is a continuous deciding one. If a judgment matrix is objective just and reasonable, the follows must be satisfied.
Capacity of expert that is knowledge and experiences of certain aspect.
Sufficient information , that is experts must be familiar with all schemes
Serious attitude that is experts must be just.
As to reliability of capacity, the dissertation evaluates it through knowledge matrix. As to reliability of information, the dissertation makes conclusion through amplifying result of before with judgment matrix. As to attitude of expert, analysis of variance is used to obtain result.
After those checks, if the judgment matrix is satisfied, the steady vector of weigh can be find through GA.
专家构造判断矩阵的过程,就是一个不断做出判断的过程。如果一个专家给出的判断矩阵是客观、公正、合理的,则应满足下列条件:
专家有能力,即专家应有相关方面足够的知识和经验。
专家有足够的信息,即专家对各个方案事实有充分的了解。
专家有认真的态度,即不会有非理性的偏好,这一点往往被人们忽视。
对于能力的可靠性,本文通过让专家构造知识矩阵来检验。对于信息(事实)可靠性,本文通过从知识矩阵检验中获得的信息可靠性与最终的判断矩阵做相关分析后给出结论。对专家的态度,本文通过对各方案的误差作方差分析后给出结论。
在完成以上检验后,如果判断矩阵是符合要求的,本文利用遗传算法求得相对稳定的权重向量。
This dissertation agrees on that the process of expert’s making judgment is like a grey box not a black box. The expert should give a knowledge matrix not a judgment matrix only. The dissertation finds that CR value is not a sufficient condition but only an essential condition through imitating expert’s judgment. So value on judgment of expert can’t be available only on CR value. The value should be from knowledge matrix. Finally the dissertation gives a method of evaluating expert’s knowledge matrix.
The process of making judgment matrix is a continuous deciding one. If a judgment matrix is objective just and reasonable, the follows must be satisfied.
Capacity of expert that is knowledge and experiences of certain aspect.
Sufficient information , that is experts must be familiar with all schemes
Serious attitude that is experts must be just.
As to reliability of capacity, the dissertation evaluates it through knowledge matrix. As to reliability of information, the dissertation makes conclusion through amplifying result of before with judgment matrix. As to attitude of expert, analysis of variance is used to obtain result.
After those checks, if the judgment matrix is satisfied, the steady vector of weigh can be find through GA.
引文
[1]赵杰.管理系统工程. [M]科学出版社,2006.
[2]黄德才,郑河荣.AHP法中判断矩阵的标度扩展构造法[J]系统工程.2003,10(1)
[3]刘业政,杨善林,刘心报.基于Rough Set理论的判断矩阵构造方法[J].系统工程学报2002,17(2).
[4]黄德才,胥琳.AHP法中判断矩阵的比例标度构造法[J].控制与决策2002,(04)
[5]刘万里,刘三阳.AHP中群决策判断矩阵的构造[J]系统工程与电子技术2005,11(1)
[6]徐泽水,达庆利.两种修正判断矩阵一致性方法的比较分析[J]东南大学学报,2002,32(6):913-916.
[7]戴建华,李军,申文明,薛恒新.模糊判断矩阵的满意一致性检验[J]系统工程与电子技术2006,28(8):1174-1176
[8]李汉华,郭均鹏.区间判断矩阵权重求解及一致性检验的目标规划模型[J]天津理工大学学报2005,21(3) 9-11
[9]叶跃祥,糜仲春,王宏宇,梁晓艳.AHP判断矩阵一致性调整的前瞻算法[J]系统工程2006,24(10):117-121
[10]王建,黄凤岗,景韶光.AHP中判断矩阵一致性调整方法研究[J]系统工程理论与实践2005,(8):85-91
[11] JuanAguaron,Josee Maria,Moreno–Jimenez. The geometric consistency index:Approximated thresholds[J]European Journal of Operational Research,2003,147(1):137-145.
[12]朱建军,刘士新,王梦光.一种新的改进不一致判断矩阵的方法[J].系统工程理论与实践,2003,23(11):95-110
[13] Dadkhan K M,ZahediF. A mathematical treatment of inconsistency in the AHP[J].Mathematical and computer modeling ,1993,17(4/5):111-123.
[14]:朱建军,王梦光,刘士新. AHP判断矩阵一性改进的若干问题研究[J].系统工程理论与实践2007,(1):18-22 ;
[15]许树柏.层次分析法原理[M].天津:天津大学出版社,1988.
[16〕吴析宗,李有文.层次分析法中矩阵的判断一致性研究[J].北京理工大学学报,1999,19(4):502一505.
[17」马维野.一种检验判断矩阵次序一致性的实用方法[J].系统工程理论与实践,1996,1600:103一105.
[18]韩光文,韩松.差异判断层次分析法[J].华中理工大学学报,1997,25(8) :l一4.
[19] Kwiesielewicz M, Uden E. Inconsistent and contradictory judgments in pairwise comparison method in the AHP [J].Computers&Operations Research, 2004,31(5):713一719.
[20〕Karapetrovic S, Rosenbloom E一A quality control approach to consistency paradoxes in AHP [J].European Journal of Operational Research, 1999,119(3):704一718.
[21] Finan J, Hurley W. A note on a method to ensure rank-order consistency in the analytic hierarchy process[J].InternationalTransactions in perational Research, 1996,3(l):99一103.
[22]杨善林,刘心报. GDSS中判断矩阵的两种集结方法[J].计算机学报2001,(1)
[23]陈侠,樊治平.基于不同偏好信息的评价专家水平研究[J].系统工程理论与实践2007,2(1)
[24]熊立,梁樑，王国华.一种群决策中确定专家判断认真程度的方法[J].系统工程2004,3(1)
[25]黄德才,郑河荣.AHP方法中判断矩阵的标度扩展构造法[J]系统工程2003-1-21(1)
[26]刘业政,杨善林,刘心报.基于Rough Set理论的判断矩阵构造方法[J]系统工程学报2002,4(1)
[27]黄德才,胥琳.AHP法中判断矩阵的比例标度构造法[J].控制与决策2002,7(2)
[28]刘万里,刘三阳.AHP中群决策判断矩阵的构造[J].系统工程与电子技术2005,11
[29]庄锦英.决策心理学[M].上海教育出版社2006。
[30]王众托.知识系统工程[M]科学出版社2005
[31]徐玖平吴巍多属性决策的理论与方法[M]北京:清华大学出版社2006.
[32]杨善林,刘业政.管理信息学[M]高等教育出版社2004
[33] Vargas L G. An overview of the analytic hierarchy process and it’s application[J]. European Journal of Operational Research ,1990,48(1).
[34]孟波有限方案模糊多目标群决策方法的研究[J]系统工程,1995,13(4):43-46.
[35]孟波,付微,一种有限方案多目标群决策方法[J]系统工程,1998,16(4):57-61.
[36] Ramanathan R , Ganesh LS. Group preference aggregation methods employed in AHP:an evaluation and an intrinsic process for deriving members’weightages[J].European Journal of Operational Research,1994,(79):249-265.
[37]熊立,王国华.一种群决策中确定专家判断认真程度的方法[J]系统工程,2004,22(3):84-87
[38]高先务,刘心报.群决策中判断矩阵不一致的原因[J]统计与决策,2008, 263(11)
[39] Korpela J, Lehmusvaara A,Tuominen M. An analytic approach to supply chain development[J].International Journal of Production Economics, 2001,71(1一3):145-155
[40] Tam M C, Tummala V M. An application of the AHP in vendor selection of a telecommunications system[J].Omega, 2001,29 (2):171一182.
[41] Saaty T L. The analytic hierarchy process[M]. New York:Megraw-Hill,1980.
[42]刘兴堂,吴晓燕.现代系统建模与仿真[M]西安:西北工业大学出版社,2001.
[43]陈来安,陆军令.系统工程原理与应用[M]北京:学术期刊出版社,1988
[44]梁梁,盛昭翰,徐南荣.一种改进的层次分析法[J]系统工程,1989,7(3):5-7
[45]马云东,胡明东.改进的AHP法及其在多目标决策中的应用[J]系统工程理论与实践,1997,17(6): 30-34,39。
[46]刘万里,雷治军关于AHP中判断矩阵一致性修正的模式识别法[J]系统工程理论与实践1997,17(11):56-59。
[47]王莲芬层次分析法中排序权数的计算方法[M]系统工程理论与实践,1987 7(2):31-37;
[48]史忠植.知识发现. [M]北京:清华大学出版社2002
[49]金菊良,魏一鸣,潘金峰.修正AHP中判断矩阵一致性的加速遗传算法[J]系统工程理论与实践,2004,1:63-69。
[2]黄德才,郑河荣.AHP法中判断矩阵的标度扩展构造法[J]系统工程.2003,10(1)
[3]刘业政,杨善林,刘心报.基于Rough Set理论的判断矩阵构造方法[J].系统工程学报2002,17(2).
[4]黄德才,胥琳.AHP法中判断矩阵的比例标度构造法[J].控制与决策2002,(04)
[5]刘万里,刘三阳.AHP中群决策判断矩阵的构造[J]系统工程与电子技术2005,11(1)
[6]徐泽水,达庆利.两种修正判断矩阵一致性方法的比较分析[J]东南大学学报,2002,32(6):913-916.
[7]戴建华,李军,申文明,薛恒新.模糊判断矩阵的满意一致性检验[J]系统工程与电子技术2006,28(8):1174-1176
[8]李汉华,郭均鹏.区间判断矩阵权重求解及一致性检验的目标规划模型[J]天津理工大学学报2005,21(3) 9-11
[9]叶跃祥,糜仲春,王宏宇,梁晓艳.AHP判断矩阵一致性调整的前瞻算法[J]系统工程2006,24(10):117-121
[10]王建,黄凤岗,景韶光.AHP中判断矩阵一致性调整方法研究[J]系统工程理论与实践2005,(8):85-91
[11] JuanAguaron,Josee Maria,Moreno–Jimenez. The geometric consistency index:Approximated thresholds[J]European Journal of Operational Research,2003,147(1):137-145.
[12]朱建军,刘士新,王梦光.一种新的改进不一致判断矩阵的方法[J].系统工程理论与实践,2003,23(11):95-110
[13] Dadkhan K M,ZahediF. A mathematical treatment of inconsistency in the AHP[J].Mathematical and computer modeling ,1993,17(4/5):111-123.
[14]:朱建军,王梦光,刘士新. AHP判断矩阵一性改进的若干问题研究[J].系统工程理论与实践2007,(1):18-22 ;
[15]许树柏.层次分析法原理[M].天津:天津大学出版社,1988.
[16〕吴析宗,李有文.层次分析法中矩阵的判断一致性研究[J].北京理工大学学报,1999,19(4):502一505.
[17」马维野.一种检验判断矩阵次序一致性的实用方法[J].系统工程理论与实践,1996,1600:103一105.
[18]韩光文,韩松.差异判断层次分析法[J].华中理工大学学报,1997,25(8) :l一4.
[19] Kwiesielewicz M, Uden E. Inconsistent and contradictory judgments in pairwise comparison method in the AHP [J].Computers&Operations Research, 2004,31(5):713一719.
[20〕Karapetrovic S, Rosenbloom E一A quality control approach to consistency paradoxes in AHP [J].European Journal of Operational Research, 1999,119(3):704一718.
[21] Finan J, Hurley W. A note on a method to ensure rank-order consistency in the analytic hierarchy process[J].InternationalTransactions in perational Research, 1996,3(l):99一103.
[22]杨善林,刘心报. GDSS中判断矩阵的两种集结方法[J].计算机学报2001,(1)
[23]陈侠,樊治平.基于不同偏好信息的评价专家水平研究[J].系统工程理论与实践2007,2(1)
[24]熊立,梁樑，王国华.一种群决策中确定专家判断认真程度的方法[J].系统工程2004,3(1)
[25]黄德才,郑河荣.AHP方法中判断矩阵的标度扩展构造法[J]系统工程2003-1-21(1)
[26]刘业政,杨善林,刘心报.基于Rough Set理论的判断矩阵构造方法[J]系统工程学报2002,4(1)
[27]黄德才,胥琳.AHP法中判断矩阵的比例标度构造法[J].控制与决策2002,7(2)
[28]刘万里,刘三阳.AHP中群决策判断矩阵的构造[J].系统工程与电子技术2005,11
[29]庄锦英.决策心理学[M].上海教育出版社2006。
[30]王众托.知识系统工程[M]科学出版社2005
[31]徐玖平吴巍多属性决策的理论与方法[M]北京:清华大学出版社2006.
[32]杨善林,刘业政.管理信息学[M]高等教育出版社2004
[33] Vargas L G. An overview of the analytic hierarchy process and it’s application[J]. European Journal of Operational Research ,1990,48(1).
[34]孟波有限方案模糊多目标群决策方法的研究[J]系统工程,1995,13(4):43-46.
[35]孟波,付微,一种有限方案多目标群决策方法[J]系统工程,1998,16(4):57-61.
[36] Ramanathan R , Ganesh LS. Group preference aggregation methods employed in AHP:an evaluation and an intrinsic process for deriving members’weightages[J].European Journal of Operational Research,1994,(79):249-265.
[37]熊立,王国华.一种群决策中确定专家判断认真程度的方法[J]系统工程,2004,22(3):84-87
[38]高先务,刘心报.群决策中判断矩阵不一致的原因[J]统计与决策,2008, 263(11)
[39] Korpela J, Lehmusvaara A,Tuominen M. An analytic approach to supply chain development[J].International Journal of Production Economics, 2001,71(1一3):145-155
[40] Tam M C, Tummala V M. An application of the AHP in vendor selection of a telecommunications system[J].Omega, 2001,29 (2):171一182.
[41] Saaty T L. The analytic hierarchy process[M]. New York:Megraw-Hill,1980.
[42]刘兴堂,吴晓燕.现代系统建模与仿真[M]西安:西北工业大学出版社,2001.
[43]陈来安,陆军令.系统工程原理与应用[M]北京:学术期刊出版社,1988
[44]梁梁,盛昭翰,徐南荣.一种改进的层次分析法[J]系统工程,1989,7(3):5-7
[45]马云东,胡明东.改进的AHP法及其在多目标决策中的应用[J]系统工程理论与实践,1997,17(6): 30-34,39。
[46]刘万里,雷治军关于AHP中判断矩阵一致性修正的模式识别法[J]系统工程理论与实践1997,17(11):56-59。
[47]王莲芬层次分析法中排序权数的计算方法[M]系统工程理论与实践,1987 7(2):31-37;
[48]史忠植.知识发现. [M]北京:清华大学出版社2002
[49]金菊良,魏一鸣,潘金峰.修正AHP中判断矩阵一致性的加速遗传算法[J]系统工程理论与实践,2004,1:63-69。