改进的离散灰色预测模型  

Improvement of a Forecasting Discrete GM(1,1)

作　　者：姚天祥[1] 刘思峰[1] 

机构地区：[1]南京航空航天大学经济与管理学院,江苏南京210016

出　　处：《系统工程》2007年第9期103-106,共4页Systems Engineering

基　　金：国家自然科学基金资助项目(70473037);教育部博士学科点科研基金资助项目(20020287001);江苏省自然科学基金重点资助项目(BK2003211);南京航空航天大学特聘教授和创新群体科研基金资助项目(1009-260812)

摘　　要：GM(1,1)模型假定序列近似服从指数规律,对于很多非线性序列的模拟出现较大偏差。本文证明了GM(1,1)模型与离散GM(1,1)模型的模拟数据的增长率都是定值,若样本数据具有相等的增长率,则应用离散GM(1,1)模型得到的模拟数据与原始序列相同。本文对离散灰色预测模型进行了改进与拓展,应用最优化方法研究了初始迭代点问题。提出了优化模型的求解算法并应用实例对算法的有效性进行了验证。研究结果表明本文建立的离散灰色拓展预测模型很大程度上提高了模型的模拟精度,能够很好地解决非线性非负序列模拟问题。The GM （1,1） model assumes the sequence is analogous to exponential law. Great error appears when it is used to simulate many non-lineal sequences. The paper proves that the growth rates of the simulated value of the GM （1,1） model and the discrete GM（1,1） model are both fixed value. If the growth rates of the primary sequence are equate, the fitted value deriving from the discrete GM（1,1） model the same as the primary sequence. The paper improves the discrete GM（1,1） model. Using the optimization method, the paper studies the initial value. The paper puts forward the solution arithmetic to the optimization and proves the efficiency of the arithmetic by means of a example. The research indicates the discrete grey extension model can greatly improve the simulated intensity and it can solve the simulated of the non-lineal non-negative sequence.

关 键 词：GM(1 1)模型 离散GM(1 1)模型 优化 

分 类 号：N941[自然科学总论—系统科学]