基于三参数区间灰数的TOPSIS决策方法
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摘要
针对决策问题的灰色系统特征,引入三参数区间灰数对评价指标进行度量。从类型一致化和无量纲化这两个方面着手对评价矩阵进行标准化。考虑到三参数区间灰数的上下界与重心点的影响,给出了基于可能度的三参数区间灰数排序方法以及三参数区间灰数距离测度方法。在此基础上,提出了基于三参数区间灰数的逼近理想解排序(technique for order preference by similarity to ideal solution,TOPSIS)决策方法,并用实例验证了其科学性与有效性。
To solve decision-making problems having the characteristics of grey systems,the three-parameter interval grey number is introduced to measure the evaluation index.The evaluation matrix is standardized from two aspects:type consistency and nondimensionalization.Taking into account the upper and lower limits as well as the center point of the three-parameter interval grey number,the sorting method and distance calculation method of the three-parameter interval grey number based on possibility are put forward.A technique for order preference by similarity to ideal solution(TOPSIS)decision-making method based on three-parameter interval grey numbers is proposed.Finally,an example is given to demonstrate the validity and effectiveness of the method.
To solve decision-making problems having the characteristics of grey systems,the three-parameter interval grey number is introduced to measure the evaluation index.The evaluation matrix is standardized from two aspects:type consistency and nondimensionalization.Taking into account the upper and lower limits as well as the center point of the three-parameter interval grey number,the sorting method and distance calculation method of the three-parameter interval grey number based on possibility are put forward.A technique for order preference by similarity to ideal solution(TOPSIS)decision-making method based on three-parameter interval grey numbers is proposed.Finally,an example is given to demonstrate the validity and effectiveness of the method.
引文
[1]WANG J,WANG J Q,ZHANG H Y,et al.Multi-criteria decision-making based on hesitant fuzzy linguistic term sets:An outranking approach[J].Knowledge-Based Systems,2015,86(1):224-236.
[2]OZER U,DEDE A.Performance evaluation of green supply chain management using integrated fuzzy multi-criteria decision making techniques[J].Computers&Industrial Engineering,2016,102(12):502-511.
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[8]LI Q,ZHAO N.Stochastic interval-grey number VIKOR method based on prospect theory[J].Grey Systems:Theory and Application,2015,5(1):105-116.
[9]SHA F,HANG J Z,YE Z X.Interval number multi-attribute grey target decision making method based on positive and negative clouts[J].Journal of Software Engineering,2016,10(3):272-278.
[10]LIU X,ZHANG Z,YIN L.A multi-objective optimization method for uncertain structures based on nonlinear interval number programming method[J].Journal of Structural Mechanics,2017,45(1):25-42.
[11]GARG H.A linear programming method based on an improved score function for interval-valued pythagorean fuzzy numbers and its application to decision-making[J].International Journal of Uncertainty Fuzziness and Knowledge-Based Systems,2018,26(1):67-80.
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[14]胡启洲,张卫华,于莉.三参数区间数研究及其在决策分析中的应用[J].中国工程科学,2007,9(3):47-51.HU Q Z,ZHANG W J,YU L.The research and application of interval numbers of three parameters[J].Engineering Science,2007,9(3):47-51.
[15]KAMFIROOZI M H,ALIREZA A,ESKANDARI M J.Application of three parameter interval grey numbers in enterprise resource planning selection[J].International Journal of Information,Security and Systems Management,2012,1(2):72-77.
[16]SAHU N K,DATTA S,MAHAPATRA S S.Decision making for selecting 3PL service provider using three parameter interval grey numbers[J].International Journal of Logistics Systems&Management,2013,14(3):261-297.
[17]WANG X,SONG B,LUO D.Multi-attribute decision-making methods with three-parameter interval grey number[J].Grey Systems:Theory and Application,2013,3(3):124-130.
[18]YANG B,ZHAO J.Correlation coefficients of hesitant threeparameter interval grey number and their applications to clustering analysis[J].Journal of Grey System,2013,25(2):139-147.
[19]MENG F,WANG N,LI B.Selection method of evaluation indicators with three-parameter interval grey number[J].Open Journal of Applied Sciences,2015,5(12):833-840.
[20]闫书丽,刘思峰,吴利丰.一种基于前景理论的三参数区间灰数型群体灰靶决策方法[J].控制与决策,2015(1):105-109.YAN S L,LIU S F,WU L F.A group grey target decision making method with three parameter interval grey number based on prospect theory[J].Control and Decision,2015(1):105-109.
[21]LI Y,ZHU S,GUO S.Multi-attribute grey target decision method with three-parameter interval grey number[J].Grey Systems:Theory and Application,2016,6(2):270-280.
[22]FU S.Three-parameter interval grey number multi-attribute decision making method based on information entropy[J].Mathematical and Computational Applications,2016,21(2):17-24.
[23]LI C,YUAN J.A new multi-attribute decision-making method with three-parameter interval grey linguistic variable[J].International Journal of Fuzzy Systems,2017,19(2):292-300.
[24]STANUJKIC D,ZAVADSKAS E K,GHORABAEE M K,et al.An extension of the EDAS method based on the use of interval grey numbers[J].Studies in Informatics&Control,2017,26(1):5-12.
[25]LI G D,YAMAGUCHI D,NAGAI M.A grey-based decisionmaking approach to the supplier selection problems[J].Mathematical and Computer Modelling,2007,46(3/4):573-581.
[26]SHAKENOVA Y.Using fuzzy logic to obtain PERT threetime estimates in oil and gas projects[J].Advanced Engineering Technology and Application,2016,5(2):29-34.
[27]FREEMAN J,CHEN T.Green supplier selection using an AHPEntropy-TOPSIS framework[J].Supply Chain Management,2015,20(3):327-340.
[28]PRAKASH C,BARUA M K.Integration of AHP-TOPSIS method for prioritizing the solutions of reverse logistics adoption to overcome its barriers under fuzzy environment[J].Journal of Manufacturing Systems,2015,37(3):599-615.
[29]AGHAJANI M M,TAHEREI G P,SULAIMAN N M,et al.Application of TOPSIS and VIKOR improved versions in a multi criteria decision analysis to develop an optimized municipal solid waste management model[J].Journal of Environmental Management,2016,166(9):109-115.
[30]陈可嘉,陈萍.“互联网+”环境下基于T-PIGN-TOPSIS的电子商务物流供应商评价[J].电子科技大学学报(社科版),2018,20(4):107-112.CHEN K J,CHEN P.Evaluation of e-commerce logistics provider based on T-PIGN-TOPSIS in Internet+environment[J].Journal of University Electronic Science and Technology of China(Social Sciences Edition),2018,20(4):107-112.
[2]OZER U,DEDE A.Performance evaluation of green supply chain management using integrated fuzzy multi-criteria decision making techniques[J].Computers&Industrial Engineering,2016,102(12):502-511.
[3]KHEMIRI R,ELBEDOUI-MAKTOUF K,GRABOT B,et al.A fuzzy multi-criteria decision-making approach for managing performance and risk in integrated procurement-production planning[J].International Journal of Production Research,2017,55(18):5305-5329.
[4]MARDANI A,ZAVADSKAS E K,KHALIFAH Z,et al.A review of multi-criteria decision-making applications to solve energy management problems:two decades from 1995to 2015[J].Renewable&Sustainable Energy Reviews,2017,71(5):216-256.
[5]ZHOU H,WANG J,ZHANG H.Grey stochastic multi-criteria decision-making approach based on prospect theory and distance measures[J].Journal of Grey System,2017,29(1):15-33.
[6]HU M L,LI L L.A novel dominance relation and application ininterval grey number decision model[J].Journal of Grey System,2014,26(1):91-98.
[7]XIE N M,XIN J H.Interval grey numbers based multi-attribute decision making method for supplier selection[J].Kybernetes,2014,43(7):1064-1078.
[8]LI Q,ZHAO N.Stochastic interval-grey number VIKOR method based on prospect theory[J].Grey Systems:Theory and Application,2015,5(1):105-116.
[9]SHA F,HANG J Z,YE Z X.Interval number multi-attribute grey target decision making method based on positive and negative clouts[J].Journal of Software Engineering,2016,10(3):272-278.
[10]LIU X,ZHANG Z,YIN L.A multi-objective optimization method for uncertain structures based on nonlinear interval number programming method[J].Journal of Structural Mechanics,2017,45(1):25-42.
[11]GARG H.A linear programming method based on an improved score function for interval-valued pythagorean fuzzy numbers and its application to decision-making[J].International Journal of Uncertainty Fuzziness and Knowledge-Based Systems,2018,26(1):67-80.
[12]卜广志,张宇文.基于三参数区间数的灰色模糊综合评判[J].系统工程与电子技术,2001,23(9):43-45,62.BU G Z,ZHANG Y W.Grey fuzzy comprehensive evaluation method based on interval numbers of three parameters[J].Systems Engineering and Electronics,2001,23(9):43-45,62.
[13]罗党.三参数区间灰数信息下的决策方法[J].系统工程理论与实践,2009,29(1):124-130.LUO D.Decision-making methods with three-parameter interval grey number[J].System Engineering-Theory&Practice,2009,29(1):124-130.
[14]胡启洲,张卫华,于莉.三参数区间数研究及其在决策分析中的应用[J].中国工程科学,2007,9(3):47-51.HU Q Z,ZHANG W J,YU L.The research and application of interval numbers of three parameters[J].Engineering Science,2007,9(3):47-51.
[15]KAMFIROOZI M H,ALIREZA A,ESKANDARI M J.Application of three parameter interval grey numbers in enterprise resource planning selection[J].International Journal of Information,Security and Systems Management,2012,1(2):72-77.
[16]SAHU N K,DATTA S,MAHAPATRA S S.Decision making for selecting 3PL service provider using three parameter interval grey numbers[J].International Journal of Logistics Systems&Management,2013,14(3):261-297.
[17]WANG X,SONG B,LUO D.Multi-attribute decision-making methods with three-parameter interval grey number[J].Grey Systems:Theory and Application,2013,3(3):124-130.
[18]YANG B,ZHAO J.Correlation coefficients of hesitant threeparameter interval grey number and their applications to clustering analysis[J].Journal of Grey System,2013,25(2):139-147.
[19]MENG F,WANG N,LI B.Selection method of evaluation indicators with three-parameter interval grey number[J].Open Journal of Applied Sciences,2015,5(12):833-840.
[20]闫书丽,刘思峰,吴利丰.一种基于前景理论的三参数区间灰数型群体灰靶决策方法[J].控制与决策,2015(1):105-109.YAN S L,LIU S F,WU L F.A group grey target decision making method with three parameter interval grey number based on prospect theory[J].Control and Decision,2015(1):105-109.
[21]LI Y,ZHU S,GUO S.Multi-attribute grey target decision method with three-parameter interval grey number[J].Grey Systems:Theory and Application,2016,6(2):270-280.
[22]FU S.Three-parameter interval grey number multi-attribute decision making method based on information entropy[J].Mathematical and Computational Applications,2016,21(2):17-24.
[23]LI C,YUAN J.A new multi-attribute decision-making method with three-parameter interval grey linguistic variable[J].International Journal of Fuzzy Systems,2017,19(2):292-300.
[24]STANUJKIC D,ZAVADSKAS E K,GHORABAEE M K,et al.An extension of the EDAS method based on the use of interval grey numbers[J].Studies in Informatics&Control,2017,26(1):5-12.
[25]LI G D,YAMAGUCHI D,NAGAI M.A grey-based decisionmaking approach to the supplier selection problems[J].Mathematical and Computer Modelling,2007,46(3/4):573-581.
[26]SHAKENOVA Y.Using fuzzy logic to obtain PERT threetime estimates in oil and gas projects[J].Advanced Engineering Technology and Application,2016,5(2):29-34.
[27]FREEMAN J,CHEN T.Green supplier selection using an AHPEntropy-TOPSIS framework[J].Supply Chain Management,2015,20(3):327-340.
[28]PRAKASH C,BARUA M K.Integration of AHP-TOPSIS method for prioritizing the solutions of reverse logistics adoption to overcome its barriers under fuzzy environment[J].Journal of Manufacturing Systems,2015,37(3):599-615.
[29]AGHAJANI M M,TAHEREI G P,SULAIMAN N M,et al.Application of TOPSIS and VIKOR improved versions in a multi criteria decision analysis to develop an optimized municipal solid waste management model[J].Journal of Environmental Management,2016,166(9):109-115.
[30]陈可嘉,陈萍.“互联网+”环境下基于T-PIGN-TOPSIS的电子商务物流供应商评价[J].电子科技大学学报(社科版),2018,20(4):107-112.CHEN K J,CHEN P.Evaluation of e-commerce logistics provider based on T-PIGN-TOPSIS in Internet+environment[J].Journal of University Electronic Science and Technology of China(Social Sciences Edition),2018,20(4):107-112.