灰色Verhulst模型背景值优化的建模方法研究

中国管理科学 ›› 2012, Vol. 20 ›› Issue (6): 154-159.

灰色Verhulst模型背景值优化的建模方法研究

熊萍萍^1,2, 党耀国¹, 姚天祥³, 崔杰²

1. 南京信息工程大学数学与统计学院, 江苏南京 210044;
2. 南京航空航天大学经济与管理学院, 江苏南京 210016;
3. 南京信息工程大学经济管理学院, 江苏南京 210044

收稿日期:2011-02-14 修回日期:2012-08-30 出版日期:2012-12-29 发布日期:2012-12-28
基金资助:
国家自然科学基金资助项目(71171116);江苏省博士后科研资助计划项目(1101094C);江苏省普通高校研究生科研创新计划资助项目(CXZZ11_0226);中央高校基本科研业务费专项资金资助;教育部人文社会科学基金项目(09YJC630129)

The Research on the Modeling Method of Background Value Optimization in Grey Verhulst Model

XIONG Ping-ping^1,2, DANG Yao-guo¹, YAO Tianxiang³, CUI Jie²

1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044,China;
3. College of Economics and Management, Nanjing University of Information Science and Technology, Nanjing 210044,China

Received:2011-02-14 Revised:2012-08-30 Online:2012-12-29 Published:2012-12-28

摘要/Abstract

摘要： 本文对传统灰色Verhulst模型背景值的误差来源进行分析,对模型的背景值进行优化,以期提高模型的模拟预测精度。基于灰色Verhulst模型时间响应式的Logistic函数形式,文章利用Logistic函数拟合模型中的一阶累加生成序列,经过一系列的数学推导,借助反向累加生成的思想,解出了Logistic函数中的三个参数,得到了灰色Verhulst模型背景值的优化公式,并建立了优化的灰色Verhulst模型。最后分别通过算例和应用实例验证本文的优化效果,结果表明,利用优化的背景值公式可以有效地提高传统灰色Verhulst模型的模拟预测精度。

关键词: 灰色Verhulst模型, Logistic函数, 背景值, 优化

Abstract: In this study, the error sources of background value of traditional grey Verhulst model and optimizes the background value of the model are analyzed, in order to improve the simulation and prediction accuracy of the model. Based on the Logistic function structure of the time response formula in the grey Verhulst model, the Logistic function is used to fit the accumulated sequence, three parameters in Logistic function are solved through a series of mathematical derivation and the idea of accumulated generating operation in opposite direction, and then the optimal formula of background value of grey Verhulst model is got and the optimal grey Verhulst model is constructed. Finally, the optimization effect in this paper is verified by an example and an application example respectively. The result shows that it can effectively improve the simulation and prediction accuracy of the traditional grey Verhulst model to use the optimization background value.

Key words: grey Verhulst model, logistic function, background value, optimization

中图分类号:

N491.5

熊萍萍, 党耀国, 姚天祥, 崔杰. 灰色Verhulst模型背景值优化的建模方法研究[J]. 中国管理科学, 2012, 20(6): 154-159.

XIONG Ping-ping, DANG Yao-guo, YAO Tianxiang, CUI Jie. The Research on the Modeling Method of Background Value Optimization in Grey Verhulst Model[J]. Chinese Journal of Management Science, 2012, 20(6): 154-159.

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