参数d迭代逼近的GM(1,1)模型及其在技术创新中的应用
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摘要
首先论述了参数d迭代逼近求解的GM(1,1)模型基本思路.其次,给出了此模型的参数估计与算法,即:1)估算出初始a_l,根据GM(1,1)模型a,c,d之间的关系,由a_l求得C_l,d_l;2)迭代d_l→d_(l+1),再计算a_(l+1),c_(l+1)及平均相对误差mape_l,mape_(l+1);3)多次迭代d_l→d_(l+1),直至|mape_(l+1)-mape_l|<ε时,可得mape最小时的最优参数a,c,d值.然后,从理论与实证方面,证明模型是无偏的,且在参数d迭代过程中,a总能取到有意义的值.最后将模型应用于企业技术创新领域之中.
The basic idea of GM(1,1)based on the iterative approximation of parameter d was first discussed.Secondly,the parameter estimation and algorithm of this model were given as follows:1)the initial value,a_l was estimated.Then c_l and di were obtained according to the relationship among a,c and d in GM(1,1)model; 2)iterated d_i to d_(l+i),and then calculated ai+i,ci+i and the average relative error mape_l,mape_(l+1); 3)iterated di to d_(l+1) repeatedly until |mape_(l+1)-mape_l|<ε.And the optimal parameter values of a,c and d could be obtained when the mape was minimal.Thirdly,the model was proved to be unbiased by theoretical and empiric al research.And parameter a obtained a meaningful value in the iterative procedure of parameter d.Finally,this model was applied to the enterprise technology innovation.
The basic idea of GM(1,1)based on the iterative approximation of parameter d was first discussed.Secondly,the parameter estimation and algorithm of this model were given as follows:1)the initial value,a_l was estimated.Then c_l and di were obtained according to the relationship among a,c and d in GM(1,1)model; 2)iterated d_i to d_(l+i),and then calculated ai+i,ci+i and the average relative error mape_l,mape_(l+1); 3)iterated di to d_(l+1) repeatedly until |mape_(l+1)-mape_l|<ε.And the optimal parameter values of a,c and d could be obtained when the mape was minimal.Thirdly,the model was proved to be unbiased by theoretical and empiric al research.And parameter a obtained a meaningful value in the iterative procedure of parameter d.Finally,this model was applied to the enterprise technology innovation.
引文
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[14]赵学敏,吴泽宁,赵春娜,等.基于粒子群算法求解GM(1,1)模型参数的研究[J].华北水利水电学院学报,2007,28(3):17-20.
[15]刘威,崔高锋.估计GM(1,1)模型参数的一种新方法[J].系统工程与电子技术,2009(2):471-474.
[16]雷鸣雳,冯祖仁.一种内涵式参数辨识的GM(1,1)新模型[J]·系统工程与电子技术,2010(2):321-325.
[17]李祚泳,张明,邓新民.基于遗传算法优化的GM(1,1)模型及效果检验[J].系统工程理论与实践,2002(8):136-139.
[18]张凌霜,王丰效.基于蚁群算法的灰色模型参数估计法[J].统计与决策,2010(15):159-160.
[19]史雪荣,王作雷.基于模糊神经网络的GM(1,1)模型[J].交通科技与经济,2008(1):55-57.
[2]Chang T S,Ku C Y,Fu H P.Grey theory analysis of online population and online game industry revenue in Taiwan[J].Technological Forecasting and Social Change,2013,80(1):175-185.
[3]Xia M,Wong W K.A seasonal discrete grey forecasting model for fashion retailing[J].KnowledgeBased Systems,2014,57:119-126.
[4]Wang Z X,Hipel K W,Wang Q,et al.An optimized NGBM(1,1)model for forecasting the qualified discharge rate of industrial wastewater in China[J].Applied Mathematical Modelling,2011,35(12):5524-5532.
[5]Zhou W,He J M.Generalized GM(1,1)model and its application in forecasting of fuel production[J].Applied Mathematical Modelling,2013,37(9):6234-6243.
[6]谭冠军.GM(1,1)模型的背景值构造方法和应用[J].系统工程理论与实践,2000,20(4):99-103.
[7]李星毅,李奎,施化吉,等.背景值优化的GM(1,1)预测模型及应用[J].电子科技大学学报,2011,40(6):911-914.
[8]何满喜,王勤.用Simpson公式构造背景值的GM(1,1)建模新方法[J].经济数学,2012,28(4):101-104.
[9]党耀国,刘思峰,刘斌.以x~((1))(n)为初始条件的GM模型[J].中国管理科学,2005,13(1):132-135.
[10]张怡,魏勇,熊常伟.灰色模型GM(1,1)的一种新优化方法[J].系统工程理论与实践,2007(4):141-146.
[11]Xie N,Liu S.Discrete grey forecasting model and its optimization[J].Applied Mathematical Modelling,2009,33(2):1173-1186.
[12]周长芹,杜迎雪,何霞.最小一乘准则GM(1,1)模型[J].廊坊师范学院学报:自然科学版,2013,13(2):29-31.
[13]何霞,刘卫锋.基于全最小一乘准则的灰色GM(1,1)模型参数估计[J].统计与决策,2012(7):30-33.
[14]赵学敏,吴泽宁,赵春娜,等.基于粒子群算法求解GM(1,1)模型参数的研究[J].华北水利水电学院学报,2007,28(3):17-20.
[15]刘威,崔高锋.估计GM(1,1)模型参数的一种新方法[J].系统工程与电子技术,2009(2):471-474.
[16]雷鸣雳,冯祖仁.一种内涵式参数辨识的GM(1,1)新模型[J]·系统工程与电子技术,2010(2):321-325.
[17]李祚泳,张明,邓新民.基于遗传算法优化的GM(1,1)模型及效果检验[J].系统工程理论与实践,2002(8):136-139.
[18]张凌霜,王丰效.基于蚁群算法的灰色模型参数估计法[J].统计与决策,2010(15):159-160.
[19]史雪荣,王作雷.基于模糊神经网络的GM(1,1)模型[J].交通科技与经济,2008(1):55-57.