灰色预测模型背景值的改进与应用

Improvement and Application of the Background Values of Grey Prediction Models

GM(1,1)灰色预测模型能够对含有不确定因素的系统进行预测,其已成为决策和系统分析的重要方法之一,但在预测中也会产生一定的误差,而背景值是导致GM(1,1)灰色预测模型产生误差的主要原因之一,为了降低灰色模型的预测误差,基于柯特斯公式和拉格朗日公式组合插值的方法建立一种新的灰色模型的背景值,将该模型应用于我国老年人口数的预测。数值实验表明,新模型极大地降低了预测误差,并增强了原模型的适用性。

The GM(1,1)grey prediction model can predict the system containing uncertain factors,which has become one of the important methods of decision-making and system analysis,but it will also produce some errors in the prediction.And background value is one of the main causes of errors in GM(1,1)grey prediction model.Aiming at solving the problem of large prediction error in GM(1,1)model,it proposed a new grey model Background values based on Lagrange formula and Background values.The model is applied to Chinese elderly population prediction.And by comparing and analyzing the prediction results,it is found that the new model can dramatically decrease the prediction error and enhance the applicability of the original model.