基于变权的GM(1,1,λ_k)模型及其应用
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摘要
文章通过把GM(1,1,λk)模型中固定权λ改进为变权λk,构造了GM(1,1,λk)模型,推导出了GM(1,1,λk)的解,然后设计了搜索法,找出最小误差解和最佳权值.再利用最小二乘拟合得到了权值的预测值,从而得到原始数据列的预测值.这种方法克服了GM(1,1,λk)模型的系统误差,进一步提高了模型的精度和适应性.最后用众多实例进行了验证和比较.结果表明本模型效果最好.
In this article the fixed weight of GM( 1,1,λ) model was modified to variable weights λk,then the GM( 1,1,λk) model was constructed,and the solution of GM( 1,1,λk) was derived. After these,we design a searching method,find the minimum error solution and the optimum weight by using this method. Then by least square fit we get the weights' predicted value,consequently obtain the original datum's predicted value. This method can overcome the system error which will occur in GM( 1,1,λ) model,and further improves the model accuracy and adaption. In the end rich living examples were used in validation and comparison,it turned out that this model gives the best results.
In this article the fixed weight of GM( 1,1,λ) model was modified to variable weights λk,then the GM( 1,1,λk) model was constructed,and the solution of GM( 1,1,λk) was derived. After these,we design a searching method,find the minimum error solution and the optimum weight by using this method. Then by least square fit we get the weights' predicted value,consequently obtain the original datum's predicted value. This method can overcome the system error which will occur in GM( 1,1,λ) model,and further improves the model accuracy and adaption. In the end rich living examples were used in validation and comparison,it turned out that this model gives the best results.
引文
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[4]李星毅,李奎,施化吉,周双全.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.
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[6]江南,刘小洋.基于Gauss公式的GM(1,1)模型的背景值构造新方法与应用[J].数学的实践与认识,2008(7):90-94.
[7]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(4):98-102.
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[11]李宏坤,赵长生,郭骋,赵利华.GM(1,1)模型改进算法及其应用研究[J].大连理工大学学报,2011(6):814-818.
[12]杨华龙,刘金霞,郑斌.灰色预测GM(1,1)模型的改进及应用[J].数学的实践与认识,2011(12):90-94.
[2]王正新,党耀国,刘思峰.基于离散指数函数优化的GM(1,1)模型[J].系统工程理论与实践,2008(2):61-67.
[3]刘乐,王洪国,王宝伟.基于背景值构造方法的GM(1,1)模型优化[J].统计与决策,2009(1):153-155.
[4]李星毅,李奎,施化吉,周双全.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.
[5]李俊峰,戴文战.基于插值和Newton-Cores公式的GM(1,1)模型的背景值构造新方法与应用[J].系统工程理论与实践,2014(10):122-126.
[6]江南,刘小洋.基于Gauss公式的GM(1,1)模型的背景值构造新方法与应用[J].数学的实践与认识,2008(7):90-94.
[7]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(4):98-102.
[8]王义闹,刘光珍,刘开第.GM(1,1)的一种逐步优化直接建模方法[J].系统工程理论与实践,2000(9):99-104.
[9]张岐山.提高灰色GM(1,1)模型精度的微粒群方法[J].中国管理科学,2007,10(5):126-129.
[10]赵越,赵嵩正.自适应GM(1,1,λ)模型及其适用范围[J].计算机工程与设计,2013,3(6):1993-1997.
[11]李宏坤,赵长生,郭骋,赵利华.GM(1,1)模型改进算法及其应用研究[J].大连理工大学学报,2011(6):814-818.
[12]杨华龙,刘金霞,郑斌.灰色预测GM(1,1)模型的改进及应用[J].数学的实践与认识,2011(12):90-94.