Hausdorff分数阶灰色预测模型的优化及应用  

Optimization and application of Hausdorff fractional grey prediction model

作　　者：李素珍 郭双冰 陈玉珍 LI Suzhen;GUO Shuangbing;CHEN Yuzhen(School of Mathematical Sciences,Henan Institute of Science and Technology,Xinxiang 453003,China)

机构地区：[1]河南科技学院数学科学学院,河南新乡453003

出　　处：《河南科技学院学报（自然科学版）》2023年第3期76-84,共9页Journal of Henan Institute of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金青年基金(12101198);河南省科技攻关项目(No.222102110104)。

摘　　要：为了提高Hausdorff分数阶灰色预测模型的预测精度,增加其在实际生活中的应用范围,论文分析影响Hausdorff分数阶灰色模型预测精度的因素,发现背景值是影响模型预测精度的主要因素;把Hausdorff分数阶灰色模型背景值的权重设为动态,构建优化的Hausdorff分数阶灰色模型,即OFHGM(1,1)模型;最后选取GM(1,1)模型、FGM(1,1)模型、FHGM(1,1)模型以及ARIMA模型作为对比模型评估OFHGM(1,1)模型在中国卫生总费用、中国人均卫生费用以及中国医院数量三个实际案例中的适用性,结果表明OFHGM(1,1)模型的预测精度高于对比模型,具有较高的适用性.In order to improve the prediction accuracy of fractional Hausdorff grey model and increase its application scope in real life,this paper firstly analyzes the factors that affect the prediction accuracy of fractional Hausdorff grey model,and finds that the background value is the main factor that affects the prediction accuracy of the model.Then the weight of background value of Hausdorff fractional grey model is designed as dynamically,and an optimized fractional Hausdorff grey model(OFHGM(1,1))is constructed.Finally,GM(1,1)model,FGM(1,1)model,FHGM(1,1)model and ARIMA model are selected as comparative models to evaluate the applicability of OFHGM(1,1)model in three actual cases of China's total health expenditure,China's per capita health expenditure and the number of hospitals in China.The result shows that the prediction accuracy of OFHGM(1,1)model is higher than that of the comparative models and has higher applicability.

关 键 词：灰色预测模型 Hausdorff分数阶 OFHGM(1 1) 背景值优化 

分 类 号：N941[自然科学总论—系统科学]