摘要
应用自动寻优定权的方法和最小二乘法,研究了灰色系统理论中灰色预测GM(1,1)模型的预测公式的形成过程,发现灰色预测GM(1,1)模型在形成预测公式时对背景值和初始值的规定是不尽合理的,且现有的改进方法对灰色预测GM(1,1)模型的改进还不尽完善.为了提高灰色预测GM(1,1)模型的预测精度,提出并使用自动寻优定权对背景值进行选择,基于最小二乘法原理对灰色预测GM(1,1)模型的初始值进行改进.实例结果表明,提出的改进方法是有效和完善的,对灰色预测GM(1,1)模型的预测精度也有较大的提高.
This paper studied the process of prediction formula of grey prediction GM（1,1） model by automatic optimization and least squares methods. It was found that artificially giving the background value and the initial value in grey prediction GM（1,1） model was quiet unreasonable and exiting modified methods of grey prediction GM（1,1） model were not well enough. In order to improve the prediction precision of grey prediction GM（1,1） model, this paper proposed and used automatic optimization to select the background va.hle and revised the initial value based on least squares theory, and then a new forecasting formula was put out. The results of empirical analysis indicates that, the proposed method is an effective and perfect, and the predictive effect of the improved grey prediction GM（1,1） model is much better.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第23期39-46,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(70972008
70971014)
