基于权重集结和相对优势关系的多属性决策方法
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摘要
分析多属性决策方法中决策矩阵规范化和属性权重计算等步骤可能对决策方法合理性造成的不良影响,为克服这些不良影响,提出一种新的多属性决策方法.该方法采用群决策模式进行赋权,在对专家意见进行一致性分析的基础上,集结各位专家给出的属性权重,通过定义备选方案在属性值为实数、区间数和语言值等不同类型属性上的相对优势关系构造判断矩阵,并以此建立方案效用值计算的线性目标规划模型,从而实现备选方案的评价和排序.实例研究表明了所提出方法的可行性和有效性.
The possible adverse influence of the steps in a multiple attribute decision making method, including normalization of the decision matrix and calculation of the attributes weights, on the reasonableness of the method is analyzed. To eliminate the bad effects caused by above mentioned steps, a new multiple attribute decision making method is proposed. The method calculats attributes weights based on a group decision making mode. The attributes weights are gained by aggregating those attributes weights given by experts whose judgements are consistent. Then by defining the relative dominance relations between schemes upon different kinds of attributes whose values are real numbers, interval numbers or linguistic values, a judgment matrix is constructed. On that basis, a linear objective programming model is established to calculate the utility value of each scheme, which is used in scheme evaluation and sorting. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed multiple attribute decision making method.
The possible adverse influence of the steps in a multiple attribute decision making method, including normalization of the decision matrix and calculation of the attributes weights, on the reasonableness of the method is analyzed. To eliminate the bad effects caused by above mentioned steps, a new multiple attribute decision making method is proposed. The method calculats attributes weights based on a group decision making mode. The attributes weights are gained by aggregating those attributes weights given by experts whose judgements are consistent. Then by defining the relative dominance relations between schemes upon different kinds of attributes whose values are real numbers, interval numbers or linguistic values, a judgment matrix is constructed. On that basis, a linear objective programming model is established to calculate the utility value of each scheme, which is used in scheme evaluation and sorting. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed multiple attribute decision making method.
引文
[1]徐泽水.不确定多属性决策方法及应用[M].北京:清华大学出版社,2004:3.(Xu Z S.Uncertain multiple attribute decision making:Methods and applications[M].Beijing:Tsinghua University Press,2004:3.)
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[7]常志朋,程龙生,刘家树.基于马田系统与TOPSIS的区间数多属性决策方法[J].系统工程理论与实践,2014,34(1):168-174.(Chang Z P,Cheng L S,Liu J S.Multiple attribute decision making method with intervals based on Mahalanobis-Taguchi system and TOPSIS method[J].Systems Engineering—Theory&Practice,2014,34(1):168-174.)
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[11]王霞,党耀国.基于Choquet积分的区间灰数多属性决策方法[J].系统工程与电子技术,2015,37(5):1106-1110.(Wang X,Dang Y G.Approach for multiple attribute decision-making with interval grey number based on Choquet integral[J].Systems Engineering and Electronics,2015,37(5):1106-1110.)
[12]吴喜之,王兆军.非参数统计方法[M].北京:高等教育出版社,1996:111-112.(Wu X Z,Wang Z J.Non-parametric statistics[M].Beijing:Higher Education Press,1996:111-112.)
[13]李霞,张绍林,张淼,等.基于新距离测度的区间数排序[J].西华大学学报:自然科学版,2008,27(1):87-90.(Li X,Zhang S L,Zhang M,et al.Rank of interval numbers based on a new distance measure[J].J of Xihua University:Natural Science Edition,2008,27(1):87-90.)
[14]姚远.运筹学[M].郑州:河南大学出版社,2013:21-22.(Yao Y.Operations research[M].Zhengzhou:Henan University Press,2013:21-22.)
[2]徐玖平,吴魏.多属性决策的理论与方法[M].北京:清华大学出版社,2006:4.(Xu J P,Wu W.Multiple attribute decision making theory and methods[M].Beijing:Tsinghua University Press,2006:4.)
[3]Churchman C W,Ackoff R L,Amoff E L.Introduction to operation research[M].New York:John Wiley and Sons,1957:2.
[4]Linstone H A,Turoff M.The delphi method:Technique and application[M].London:Addiaon Wesley,1975:3.
[5]Saaty T L.The Analytic hierarchy process[M].New York:Mc Graw-Hill Company,1980:2.
[6]Hwang C L,Yoon K S.Multiple attribute decision-making methods and applications:A state-of-the-art survey[M].Berlin:Springer,1981:58.
[7]常志朋,程龙生,刘家树.基于马田系统与TOPSIS的区间数多属性决策方法[J].系统工程理论与实践,2014,34(1):168-174.(Chang Z P,Cheng L S,Liu J S.Multiple attribute decision making method with intervals based on Mahalanobis-Taguchi system and TOPSIS method[J].Systems Engineering—Theory&Practice,2014,34(1):168-174.)
[8]张方伟,王炜,赵德.一种基于分层法的区间数多属性决策方法及应用[J].系统工程理论与实践,2014,34(11):2881-2884.(Zhang F W,Wang W,Zhao D.Method for multiple attributes decision-making with intervals based on layer method and its application[J].Systems Engineering—Theory&Practice,2014,34(11):2881-2884.)
[9]朱丽,朱传喜,张小芝.基于粗糙集的犹豫模糊多属性决策方法[J].控制与决策,2014,29(7):1335-1339.(Zhu L,Zhu C X,Zhang X Z.Method for hesitant fuzzy multi-attribute decision making based on rough sets[J].Control and Decision,2014,29(7):1335-1339.)
[10]陈小卫,王文双,宋贵宝,等.基于模糊偏序关系的混合型多属性决策方法[J].系统工程与电子技术,2012,34(3):529-533.(Chen X W,Wang W S,Song G B,et al.Hybrid multi-attribute decision making based on fuzzy preference relation[J].Systems Engineering and Electronics,2012,34(3):529-533.)
[11]王霞,党耀国.基于Choquet积分的区间灰数多属性决策方法[J].系统工程与电子技术,2015,37(5):1106-1110.(Wang X,Dang Y G.Approach for multiple attribute decision-making with interval grey number based on Choquet integral[J].Systems Engineering and Electronics,2015,37(5):1106-1110.)
[12]吴喜之,王兆军.非参数统计方法[M].北京:高等教育出版社,1996:111-112.(Wu X Z,Wang Z J.Non-parametric statistics[M].Beijing:Higher Education Press,1996:111-112.)
[13]李霞,张绍林,张淼,等.基于新距离测度的区间数排序[J].西华大学学报:自然科学版,2008,27(1):87-90.(Li X,Zhang S L,Zhang M,et al.Rank of interval numbers based on a new distance measure[J].J of Xihua University:Natural Science Edition,2008,27(1):87-90.)
[14]姚远.运筹学[M].郑州:河南大学出版社,2013:21-22.(Yao Y.Operations research[M].Zhengzhou:Henan University Press,2013:21-22.)
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