利用非齐次指数函数构造GM(1,1)模型背景值的新方法  

A New Approach of Utilizing Non-homogeneous Exponential Function to Construct GM(1,1) Model Background Value

作　　者：高宁[1,2] 高彩云[1] 

机构地区：[1]河南城建学院测绘工程学院,河南平顶山467044 [2]东华理工大学江西省数字国土重点实验室,南昌330013

出　　处：《统计与决策》2017年第17期24-27,共4页Statistics & Decision

基　　金：国家自然科学基金资助项目(51474217);江西省数字国土重点实验室开放研究基金资助项目(DLLJ201508);矿山空间信息技术国家测绘地理信息局重点实验室基金资助项目(KLM201306);河南省高等学校重点科研基金项目(16A420001)

摘　　要：文章以灰色GM(1,1)模型背景值的优化为研究目的,讨论了传统背景值构造方法适用于低增长指数序列、对高增长指数序列拟合产生滞后误差的原因,提出了利用非齐次指数函数x^((1))(t)=A×e^(B×t)+C在区间[k-1,k]上与横坐标轴所围实际面积来构造背景值的新方法,并对其合理性进行了证明;在不同发展系数a条件下,比较了背景值构造方法对模拟和预测精度的影响,给出了新背景值条件下GM(1,1)模型的适用范围;大量的数据模拟和模型比较表明,新背景值构造方法提高了背景值的精确性及灰预测模型的拟合精度和预测精度。This paper takes the optimization of grey GM （1,1） model background value as the research purpose, and discusses the factors that brings delay error to high growth index series although the traditional background value construction method is suitable for low growth index series. At the same time the paper proposes utilizing non-homogeneous exponential function [x（1）（t）= A· eB· t＋C] in the interval [[k-1,k]] and the area enclosed with the abscissa axis to construct background value, and also verifies the rationality. Under the situation of different developing coefficient [a], the paper compares the influence that background-value building method brings upon simulation and prediction precision, and finally offers the application scope of GM （1,1） model under the new background value. A large number of data simulation and model comparisons show that the new background-value construction method improves the accuracy of background value, and fitting precision and prediction precision of the grey prediction model as well.

关 键 词：GM(1 1) 非齐次指数函数 背景值 发展系数a 预测 

分 类 号：N941[自然科学总论—系统科学]