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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (2): 343-354.doi: 10.3969/j.issn.1005-3085.2025.02.009

• • 上一篇    下一篇

一种含参变量函数变换的新型灰色预测模型

陈心愿1,2,  陈友军1   

  1. 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
  • 收稿日期:2022-09-13 接受日期:2023-03-20 出版日期:2025-04-15 发布日期:2025-06-15
  • 通讯作者: 陈友军 E-mail: chenzyw@126.com
  • 基金资助:
    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).

A New Grey Prediction Model with Parameter Function Transformation

CHEN Xinyuan1,2,  CHEN Youjun1   

  1. 1. School of Mathmatics and Information, China West Normal University, Nanchong 637002
    2. Nanchong Senior High School, Nanchong 637001
  • Received:2022-09-13 Accepted:2023-03-20 Online:2025-04-15 Published:2025-06-15
  • Contact: Y. Chen. E-mail address: chenzyw@126.com
  • Supported by:
    The Natural Science Foundation of Sichuan Provincial Department of Education (18ZA0469); the Elite Scientific Research Fund Project of West China Normal University (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${\rm GM}(1,1)$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。

关键词: 函数变换, 级比偏差, 相对误差, 预测精度

Abstract:

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 ${\rm GM}(1,1)$ 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.

Key words: function transformation, class ratio deviation, relative error, prediction accuracy

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