GM(1 ,1) 模型的几种基本形式及其适用范围研究

doi:10.3969/1.issn.1001-506X.2014.03.16

系统工程与电子技术 ›› 2014, Vol. 36 ›› Issue (3): 501-508.doi: 10.3969/1.issn.1001-506X.2014.03.16

GM(1 ,1) 模型的几种基本形式及其适用范围研究

刘思峰, 曾波, 刘解放, 谢乃明

1.南京航空航天大学灰色系统研究所，江苏南京 210016;
2.重庆工商大学商务策划学院，重庆 400067

出版日期:2014-03-24 发布日期:2010-01-03
基金资助:
null

Several basic models of GM(1 ,1) and their applicable bound

LIU Sifeng, ZENG Bo, LIU Jiefang, XIE Naiming

l. Institute for Grey Systems Studies , Nanjing University of Aeronautics and Astronautics, Nanjing 210016 , China; 2. College of Business Planning , Chongqing Technology and Business University , Chongging 400067, China

Online:2014-03-24 Published:2010-01-03

摘要/Abstract

摘要：

定义了GM(1,1)模型的 4种基本形式:均值GM(1,1)模型(even grey model,EGMD,原始差分GM(1,1)模型(original difference grey model, ODGM),均值差分 GM(1,1)模型(even diflerence grey model， EDGM)和离散GM(1,1)模型(discrele grey model,DGM),并深入研究了不同模型的性质和特点,证明了不同形式的模型相互等价。通过对齐次指数序列、非指数增长序列和振荡序列的模拟分析,明确了不同模型的适用范围:ODGM、EDGM和DGM均适用于齐次指数序列和近似齐次指数序列的情形。微分、差分混合形态的 EGM适宜于非指数增长序列和振荡序列的情形。相关结论可作为实际建模过程中选择模型的参考和依据。

关键词: GM(1,1)模型, 基本形式, 适用范图

Abstract:

The definitions of 4 basic models of GM(1,1), such as even grey model (EGM) , original differ-ence grey model (ODGM), even difference grey model (EDCM) ,and discrete grey model (DGM) , are put forward, The properties and characteristics of different models are studied and the equivalences of different modelsare proved. The applicable bounds of different models are studied by simulation and analysis with homogeneous exponential sequences, nonhomogeneous exponential increasing sequences, and vibration sequences. The main conclusions are obtained as follows: ODCM, EDCM and DCM are suitable for homoeneous exponential sequences or sequences which are close to the homogeneous exponential sequences. The EGM are suitable for nonhomogeneous exponential increasing seguences and vibration seguences.

Key words: GM(1, 1) ;basic models ;applicable bound

中图分类号:

N 941.5

刘思峰, 曾波, 刘解放, 谢乃明. GM(1 ,1) 模型的几种基本形式及其适用范围研究[J]. 系统工程与电子技术, 2014, 36(3): 501-508.

LIU Sifeng, ZENG Bo, LIU Jiefang, XIE Naiming. Several basic models of GM(1 ,1) and their applicable bound[J]. Systems Engineering and Electronics, 2014, 36(3): 501-508.

GM(1 ,1) 模型的几种基本形式及其适用范围研究

Several basic models of GM(1 ,1) and their applicable bound

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