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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 ›› 2021, Vol. 38 ›› Issue (1): 38-48.doi: 10.3969/j.issn.1005-3085.2021.01.004

• • 上一篇    下一篇

一类改进的GOM(1,1)模型及其应用

张   锴1,   王成勇2,   贺丽娟1   

  1. 1- 文华学院数学科学系，武汉  430074
    2- 湖北文理学院数学与统计学院，襄阳  441053
  • 收稿日期:2018-05-29 接受日期:2019-05-15 出版日期:2021-02-15 发布日期:2021-04-15
  • 通讯作者: 贺丽娟 E-mail: 23518427@qq.com
  • 基金资助:
    国家自然科学基金 (71371066)；湖北省教育厅科学研究计划指导性计划 (B2017347)；文华学院教学研究项目 (2019jcjy15).

An Improved GOM(1,1) Model and Its Application

ZHANG Kai1,   WANG Cheng-yong2,   HE Li-juan1   

  1. 1- Department of Mathematics Science, Wenhua College, Wuhan 430074
    2- School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang 441053
  • Received:2018-05-29 Accepted:2019-05-15 Online:2021-02-15 Published:2021-04-15
  • Contact: L. He. E-mail address: 23518427@qq.com
  • Supported by:
    The National Natural Science Foundation of China (71371066); the Science and Technology Foundation of Education Commission of Hubei Province (B2017347); the Teaching and Research Project of Wenhua College (2019jcjy15).

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摘要： 本文考虑非负递减序列的建模预测问题．考虑到灰作用量会随着时间和空间的变化而发展变化，将灰作用量近似看作为时间的线性函数从而构建了灰作用量优化的GOM(1,1)模型．结合灰色预测模型数据序列的非齐次指数特性，利用积分推导出GOM(1,1)模型的最优化背景值．以原始序列和模拟序列的平均相对误差平方和最小为原则，确定最优的时间响应函数表达式，最终形成了完整的GOM(1,1)模型的改进算法．最后，通过实例的验证和对比，说明优化模型的有效性与实用性．

关键词: GOM(1,1)模型, 灰作用量, 背景值, 时间响应函数

Abstract: In this paper, the modeling and prediction problem of non-negative decreasing sequence are considered. Considering that a grey action will develop and change with the change of the time and space, the grey action is approximately regarded as a linear function of time to construct a GOM(1,1) model with grey action optimization. The optimal background value of GOM(1,1) model is derived by integration based on the non-homogeneous exponential characteristics of the data series of the grey prediction model. Based on the principle of minimum square sum of mean relative error between an original sequence and a simulated sequence, the optimal time response function expression was determined, and the improved algorithm of complete GOM(1,1) model was finally formed. Finally, the effectiveness and practicability of the improved model are verified by an application example.

Key words: GOM(1,1) model, grey action quantity, the background value, time response function

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