基于广义灰色激励因子的多源不确定性指标动态综合评价模型研究
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摘要
由于多数评价指标的数据来源多、存储方式不一、处理方法各异等,使得其具有多源不确定性(multisource uncertainty,MSU)特点,具体表现为指标评价值往往包括灰数、模糊数、区间值模糊数以及白数等。针对此类指标的评价问题,提出了新的基于广义灰色激励因子的多源不确定性指标(multi-source uncertain index,MSUI)动态综合评价模型,首先引入广义灰数的基本理念,将传统的灰色绝对关联模型扩展到评价指标为广义灰数的形式,由此得出各个时间段指标的广义灰色激励因子;然后根据指标信息不对称的特点,构建基于MSUI的广义灰色熵权模型,求解出各个指标的广义灰色熵权;接着在广义灰色激励因子与广义灰色熵权的基础上,建立基于广义灰色激励因子的MSUI动态综合评价模型;最后结合案例研究证明了模型的有效性与可行性。
Most of the evaluation indexes have the characteristics of multi-source uncertainty(MSU)because the data of them have much source,different storage mode and handling methods.It is reflected by the evaluation values including grey number,fuzzy number,interval-valued fuzzy number and white number.For the evaluation problem of such indexes,we propose a new dynamic comprehensive evaluation model of multi-source uncertain index(MSUI)based on the generalized grey incentive factors.At first,we introduce the generalized grey number and extend the traditional grey absolute correlation model to the form of evaluation indexes of generalized grey number,thus determine the generalized grey incentive factors.Then according to the characteristic of information asymmetry of indexes,we build the generalized grey entropy weight model based on the MSUI,and determine the generalized grey entropy weight of each index.Next,we build the dynamic comprehensive evaluation model of MSUI based on the generalized grey incentive factors with the generalized grey incentive factors and the generalized grey entropy weight.Finally,it proves the effectiveness and feasibility of the model through the case study.
Most of the evaluation indexes have the characteristics of multi-source uncertainty(MSU)because the data of them have much source,different storage mode and handling methods.It is reflected by the evaluation values including grey number,fuzzy number,interval-valued fuzzy number and white number.For the evaluation problem of such indexes,we propose a new dynamic comprehensive evaluation model of multi-source uncertain index(MSUI)based on the generalized grey incentive factors.At first,we introduce the generalized grey number and extend the traditional grey absolute correlation model to the form of evaluation indexes of generalized grey number,thus determine the generalized grey incentive factors.Then according to the characteristic of information asymmetry of indexes,we build the generalized grey entropy weight model based on the MSUI,and determine the generalized grey entropy weight of each index.Next,we build the dynamic comprehensive evaluation model of MSUI based on the generalized grey incentive factors with the generalized grey incentive factors and the generalized grey entropy weight.Finally,it proves the effectiveness and feasibility of the model through the case study.
引文
[1]郭亚军.综合评价理论、方法及应用[M].北京:科学出版社,2012.GUO Y J.Comprehensive evaluation theory,method and application[M].Beijing:Science Press,2012.
[2]郭亚军,马凤妹,董庆兴.无量纲化方法对拉开档次法的影响分析[J].管理科学学报,2011,14(5):19-28.GUO Y J,MA F M,DONG Q X.Analysis of influence of dimensionless methods on deviation maximization method[J].Journal of Management Science in China,2011,14(5):19-28.
[3]岳峰,苏兆品,陆阳,等.基于模糊软集合的软件质量综合评价方法[J].系统工程与电子技术,2013,35(7):1460-1466.YUE F,SU Z P,LU Y,et al.Comprehensive evaluation of software quality based on fuzzy soft sets[J].Systems Engineering and Electronics,2013,35(7):1460-1466.
[4]郭亚军,何志勇,董飞飞.基于双重优势的自主式综合评价方法[J].系统工程与电子技术,2011,33(12):2668-2671.GUO Y J,HE Z Y,DONG F F.Self-determination comprehensive evaluation approach based on dual superiority[J].Systems Engineering and Electronics,2011,33(12):2668-2671.
[5]刘光才,赖汪湾.基于粗糙集理论及灰色关联分析模型的我国民航发展水平综合评价[J].数学的实践与认识,2017,47(22):46-57.LIU G C,LAI W W.Comprehensive evaluation of China’s civil aviation development level based on rough set theory and grey correlative analysis method[J].Mathematics in Practice and Theory,2017,47(22):46-57.
[6]高炜,张庆普,敦晓彪,等.基于改进的可拓层次分析法和动态加权的航天高技术综合评价研究[J].系统工程与电子技术,2016,38(1):102-109.GAO W,ZHANG Q P,DUN X B,et al.Comprehensive assessment of advanced military aerospace technologies based on improved EAHP and dynamic weighting[J].Systems Engineering and Electronics,2016,38(1):102-109.
[7]郭亚军,唐海勇,曲道钢.基于最小方差的动态综合评价方法及应用[J].系统工程与电子技术,2010,32(6):1225-1228.GUO Y J,TANG H Y,QU D G.Dynamic comprehensive evaluation method and its application based in minimal variability[J].Systems Engineering and Electronics,2010,32(6):1225-1228.
[8]李旭辉,朱启贵.生态主体功能区经济社会发展绩效动态综合评价[J].中央财经大学学报,2017(7):96-105.LI X H,ZHU Q G.Research on the dynamic comprehensive evaluation system of economic and social development performance of ecological major function area[J].Journal of Central University of Finance&Economics,2017(7):96-105.
[9]李美娟,陈国宏,林志炳,等.基于理想解法的动态评价方法研究[J].中国管理科学,2015,23(10):156-161.LI M J,CHEN G H,LIN Z B,et al.Dynamic evaluation method based in TOPSIS[J].Chinese Journal of Management Science,2015,23(10):156-161.
[10]张发明.基于双重激励模型的动态综合评价方法及应用[J].系统工程学报,2013,28(2):248-255.ZHANG F M.Dynamic comprehensive evaluation method based on double incentives model and its application[J].Journal of System Engineering,2013,28(2):248-255.
[11]马赞福,郭亚军,张发明,等.一种基于增益水平激励的动态综合评价方法[J].系统工程学报,2009,24(2):243-247.MA Z F,GUO Y J,ZHANG F M,et al.Method of dynamic comprehensive evaluation based on gain level inspiriting[J].Journal of System Engineering,2009,24(2):243-247.
[12]边旭,田厚平,郭亚军.具有激励特征的供应商动态评价方法[J].南开管理评论,2004,7(5):87-90.BIAN X,TIAN H P,GUO Y J.The supplier dynamic evaluation method with the character of stimulation[J].Nankai Business Review,2004,7(5):87-90.
[13]SCHOOTEN F V.De ratiociniis in Ludo Ale[J].Exercitationum Mathematicarum,2014:521-535.
[14]YUSHKEVICH A P.Nikolas Bernoulli and the publication of《Arsconjectandi》by Jacob Bernoulli[J].Theory of Probability&Its Applications,1986,31(2):333-352.
[15]ROSENBLATT M.A central limit theorem and a strong mixing condition[J].Proceedings of the National Academy of Sciences of the United States of America,1956,42(1):43-47.
[16]LAPLACE P S.Oeuvres de Laplace:théorie analytique des probabilités[M].America:Nabu Press,2010:1-902.
[17]KOLMOGOROV A N.Foundations of the theory of probability[J].Genus,1950,77(1/4):303.
[18]RESAT H,WILEY H S,DIXON D A.Probability-weighted dynamic Monte-Carlo method for reaction kinetics simulations[J].Journal of Physical Chemistry B,2016,105(44):11026-11034.
[19]PATERA R P.General method for calculating satellite collision probability[J].Journal of Guidance Control&Dynamics,2015,24(4):716-722.
[20]ZADEH L A.Fuzzy sets[J].Information&Control,1965,8(3):338-353.
[21]ATANASSOV K T.New operations defined over the intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1994,61(2):137-142.
[22]CHANG S S L,ZADEH L A.On fuzzy mapping and control[J].IEEE Trans.on Systems Man&Cybernetics,1972,SMC-2(1):30-34.
[23]DENG J L.Control problems of grey systems[J].Systems&Control Letters,1982,1(5):288-294.
[24]TRIPATHY S,TRIPATHY D K.Multi-attribute optimization of machining process parameters in powder mixed electro-discharge machining using TOPSIS and grey relational analysis[J].Engineering Science&Technology an International Journal,2016,19(1):62-70.
[25]TSAI S B.Using grey models for forecasting China’s growth trends in renewable energy consumption[J].Clean Technologies&Environmental Policy,2016,18(2):563-571.
[26]FANG Z,ZHANG Q,CAI J,et al.On general standard grey number representation and operations for multi-type uncertain data[C]∥Proc.of the International Conference on Grey Sys-tems and Intelligent Services,2017:19-26.
[27]刘思峰,党耀国,方志耕,等.灰色系统理论及其应用[M].北京:科学出版社,2015.LIU S F,DANG Y G,FANG Z G,et al.The theory of grey system and its application[M].Beijing:Science Press,2015.
[28]钱丽丽,刘思峰,谢乃明.基于熵权和区间灰数信息的灰色聚类模型[J].系统工程与电子技术,2016,38(2):352-356.QIAN L L,LIU S F,XIE N M.Grey clustering model based on entropy-weight and grey numbers[J].Systems Engineering and Electronics,2016,38(2):352-356.
[29]刘思峰,方志耕,谢乃明.基于核和灰度的区间灰数运算法则[J].系统工程与电子技术,2010,32(2):313-316.LIU S F,FANG Z G,XIE N M.Algorithm rules of interval grey numbers based on the“Kernel”and the degree of greyness of grey numbers[J].Systems Engineering and Electronics,2010,32(2):313-316.
[2]郭亚军,马凤妹,董庆兴.无量纲化方法对拉开档次法的影响分析[J].管理科学学报,2011,14(5):19-28.GUO Y J,MA F M,DONG Q X.Analysis of influence of dimensionless methods on deviation maximization method[J].Journal of Management Science in China,2011,14(5):19-28.
[3]岳峰,苏兆品,陆阳,等.基于模糊软集合的软件质量综合评价方法[J].系统工程与电子技术,2013,35(7):1460-1466.YUE F,SU Z P,LU Y,et al.Comprehensive evaluation of software quality based on fuzzy soft sets[J].Systems Engineering and Electronics,2013,35(7):1460-1466.
[4]郭亚军,何志勇,董飞飞.基于双重优势的自主式综合评价方法[J].系统工程与电子技术,2011,33(12):2668-2671.GUO Y J,HE Z Y,DONG F F.Self-determination comprehensive evaluation approach based on dual superiority[J].Systems Engineering and Electronics,2011,33(12):2668-2671.
[5]刘光才,赖汪湾.基于粗糙集理论及灰色关联分析模型的我国民航发展水平综合评价[J].数学的实践与认识,2017,47(22):46-57.LIU G C,LAI W W.Comprehensive evaluation of China’s civil aviation development level based on rough set theory and grey correlative analysis method[J].Mathematics in Practice and Theory,2017,47(22):46-57.
[6]高炜,张庆普,敦晓彪,等.基于改进的可拓层次分析法和动态加权的航天高技术综合评价研究[J].系统工程与电子技术,2016,38(1):102-109.GAO W,ZHANG Q P,DUN X B,et al.Comprehensive assessment of advanced military aerospace technologies based on improved EAHP and dynamic weighting[J].Systems Engineering and Electronics,2016,38(1):102-109.
[7]郭亚军,唐海勇,曲道钢.基于最小方差的动态综合评价方法及应用[J].系统工程与电子技术,2010,32(6):1225-1228.GUO Y J,TANG H Y,QU D G.Dynamic comprehensive evaluation method and its application based in minimal variability[J].Systems Engineering and Electronics,2010,32(6):1225-1228.
[8]李旭辉,朱启贵.生态主体功能区经济社会发展绩效动态综合评价[J].中央财经大学学报,2017(7):96-105.LI X H,ZHU Q G.Research on the dynamic comprehensive evaluation system of economic and social development performance of ecological major function area[J].Journal of Central University of Finance&Economics,2017(7):96-105.
[9]李美娟,陈国宏,林志炳,等.基于理想解法的动态评价方法研究[J].中国管理科学,2015,23(10):156-161.LI M J,CHEN G H,LIN Z B,et al.Dynamic evaluation method based in TOPSIS[J].Chinese Journal of Management Science,2015,23(10):156-161.
[10]张发明.基于双重激励模型的动态综合评价方法及应用[J].系统工程学报,2013,28(2):248-255.ZHANG F M.Dynamic comprehensive evaluation method based on double incentives model and its application[J].Journal of System Engineering,2013,28(2):248-255.
[11]马赞福,郭亚军,张发明,等.一种基于增益水平激励的动态综合评价方法[J].系统工程学报,2009,24(2):243-247.MA Z F,GUO Y J,ZHANG F M,et al.Method of dynamic comprehensive evaluation based on gain level inspiriting[J].Journal of System Engineering,2009,24(2):243-247.
[12]边旭,田厚平,郭亚军.具有激励特征的供应商动态评价方法[J].南开管理评论,2004,7(5):87-90.BIAN X,TIAN H P,GUO Y J.The supplier dynamic evaluation method with the character of stimulation[J].Nankai Business Review,2004,7(5):87-90.
[13]SCHOOTEN F V.De ratiociniis in Ludo Ale[J].Exercitationum Mathematicarum,2014:521-535.
[14]YUSHKEVICH A P.Nikolas Bernoulli and the publication of《Arsconjectandi》by Jacob Bernoulli[J].Theory of Probability&Its Applications,1986,31(2):333-352.
[15]ROSENBLATT M.A central limit theorem and a strong mixing condition[J].Proceedings of the National Academy of Sciences of the United States of America,1956,42(1):43-47.
[16]LAPLACE P S.Oeuvres de Laplace:théorie analytique des probabilités[M].America:Nabu Press,2010:1-902.
[17]KOLMOGOROV A N.Foundations of the theory of probability[J].Genus,1950,77(1/4):303.
[18]RESAT H,WILEY H S,DIXON D A.Probability-weighted dynamic Monte-Carlo method for reaction kinetics simulations[J].Journal of Physical Chemistry B,2016,105(44):11026-11034.
[19]PATERA R P.General method for calculating satellite collision probability[J].Journal of Guidance Control&Dynamics,2015,24(4):716-722.
[20]ZADEH L A.Fuzzy sets[J].Information&Control,1965,8(3):338-353.
[21]ATANASSOV K T.New operations defined over the intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1994,61(2):137-142.
[22]CHANG S S L,ZADEH L A.On fuzzy mapping and control[J].IEEE Trans.on Systems Man&Cybernetics,1972,SMC-2(1):30-34.
[23]DENG J L.Control problems of grey systems[J].Systems&Control Letters,1982,1(5):288-294.
[24]TRIPATHY S,TRIPATHY D K.Multi-attribute optimization of machining process parameters in powder mixed electro-discharge machining using TOPSIS and grey relational analysis[J].Engineering Science&Technology an International Journal,2016,19(1):62-70.
[25]TSAI S B.Using grey models for forecasting China’s growth trends in renewable energy consumption[J].Clean Technologies&Environmental Policy,2016,18(2):563-571.
[26]FANG Z,ZHANG Q,CAI J,et al.On general standard grey number representation and operations for multi-type uncertain data[C]∥Proc.of the International Conference on Grey Sys-tems and Intelligent Services,2017:19-26.
[27]刘思峰,党耀国,方志耕,等.灰色系统理论及其应用[M].北京:科学出版社,2015.LIU S F,DANG Y G,FANG Z G,et al.The theory of grey system and its application[M].Beijing:Science Press,2015.
[28]钱丽丽,刘思峰,谢乃明.基于熵权和区间灰数信息的灰色聚类模型[J].系统工程与电子技术,2016,38(2):352-356.QIAN L L,LIU S F,XIE N M.Grey clustering model based on entropy-weight and grey numbers[J].Systems Engineering and Electronics,2016,38(2):352-356.
[29]刘思峰,方志耕,谢乃明.基于核和灰度的区间灰数运算法则[J].系统工程与电子技术,2010,32(2):313-316.LIU S F,FANG Z G,XIE N M.Algorithm rules of interval grey numbers based on the“Kernel”and the degree of greyness of grey numbers[J].Systems Engineering and Electronics,2010,32(2):313-316.