一种含参变量函数变换的新型灰色预测模型  

A New Grey Prediction Model with Parameter Function Transformation

作　　者：陈心愿 陈友军[1] CHEN Xinyuan;CHEN Youjun(School of Mathmatics and Information,China West Normal University,Nanchong 637002;Nanchong Senior High School,Nanchong 637001)

机构地区：[1]西华师范大学数学与信息学院,南充637002 [2]四川省南充高级中学,南充637001

出　　处：《工程数学学报》2025年第2期343-354,共12页Chinese Journal of Engineering Mathematics

基　　金：四川省教育厅自然科学基金(18ZA0469);西华师范大学教学英才科研基金(17YC370)。

摘　　要：提出了一类含参变量函数变换,证明了使用该方法可在一定程度上缩小序列的级比偏差,分别给出了单调递增和单调递减序列缩小级比偏差的充要条件。为了保证还原后仍具有高建模精度,进一步研究了含参变量函数变换还原不扩大相对误差的函数特征。最后结合GM(1, 1)建模方法进行建模,实例验证了这类含参变量函数变换方法具有还原不扩大相对误差的特性,且能提高短期预测精度。A class of function transformation with reference variables is proposed,and it is proved that the method can reduce the step ratio deviation of the sequence to a certain extent.The sufficient and necessary conditions for reducing the step ratio deviation of the monotonically increasing and monotonically decreasing sequences are given respectively.In order to ensure that the modeling accuracy is still improved after the reduction,the function characteristics of non-expanding relative error in the transformation reduction of function with reference variables are further studied.Finally,the GM(1,1)modeling method is used to build the model.The example verifies that this kind of parametric variable function transformation method has the characteristics of reducing without expanding the relative error,and can improve the short-term prediction accuracy.

关 键 词：函数变换 级比偏差 相对误差 预测精度 

分 类 号：N941.5[自然科学总论—系统科学]