基於不動點的新資訊GM(1,1)模型

The New Information GM(1,1) Based on the Fixed Points

姚天祥(Tian-Xiang Yao) ； 劉思峰(Si-Feng Liu)

《管理科學與統計決策》 5卷2期 (2008/06) Pp. 52-58

https://doi.org/10.6704/JMSSD.2008.5.2.52

摘要

由於新資訊比老資訊通常更能反映系統的發展趨勢，本文提出了基於不動點的新資訊GM(1,1)模型(NFGM)。對該模型的相關特性進行了研究並進一步給出了分段修正NFGM模型(SFNGM)的建模步驟。結果表明NFGM模型的模擬序列增長率是等比序列；數乘變換不改變NFGM模型的模擬精度；序列初始值不改變發展係數和模擬值。應用實例表明SFNGM模型能夠顯著提高模擬精度。

關鍵字

GM 1,1模型 ； 不動點 ； 新信息 ； 數乘變換

並列摘要

When simulating the development tendency of the system, the new information is usually more useful than the old information. The paper put forward the new information GM(1,1) model (NFGM) based on the fixed points. It studied the properties of the NFGM model. The paper put forward the segmental corrected NFGM model (SFNGM) and gave the modeling steps. The results indicates the grow rates sequence of the simulation of NFGM model is a geometric sequence. The multiple transformations do not change the simulation precision of the simulation value sequence. The initial value of the raw sequence do not change the development coefficient and the simulation values. A case of study indicates the SFNGM model can obviously improve the simulation precision.

並列關鍵字

Grey System ； Fixed points ； New information ； Multiple transformations

參考文獻

Liu Sifeng,Lin Yi.(1998).An Introduction to Grey Systems: Foundations, Methodology and Applications.Grove City:IIGSS academic.

Liu Sifeng,Lin Yi.(2005).Grey Information: Theory and Practical Applications.London:Springer-Verlag London Ltd.

Liu Sifeng,Deng Julong.(1999).The range suitable for GM (1,1).The Journal of Grey System.1,131-138.

謝乃明、劉思峰(2005)。離散GM(1,1)模型與灰色預測模型建模機理。系統工程理論與實踐。1，93-99。

姚天祥、劉思峰(2007)。改進的離散灰色預測模型。系統工程。9，103-106。