The Essential of GM(1,1) Model

IF 1 4区工程技术 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Grey System Pub Date : 2007-09-01 DOI:10.30016/JGS.200709.0004

Xiaoxuan Zhang

引用次数: 1

Abstract

This paper reveals that GM(1,1) model is actually constructed according to the first order linearly differential equation, it is an equation that exponential sequences satisfy, so the essential of GM(1,1) model is an exponential sequence model. Though GM(1,1) model is constructed according to the first order linearly differential equation, both are not the same, this paper shows their features in common and differences. In addition, this paper proposes that models constructed according to the first order linearly differential equation are not unique, the author constructs another exponential sequence model, we might as well call it grey exponential model(GEM), it can replace GM(1,1) model for predicting of grey systems.

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GM(1,1)模型的本质

本文揭示了GM(1,1)模型实际上是根据一阶线性微分方程构造的，它是一个指数序列满足的方程，因此GM(1,1)模型的本质是指数序列模型。虽然GM(1,1)模型是根据一阶线性微分方程构造的，但两者并不相同，本文给出了它们的共同点和不同点。此外，本文提出了由一阶线性微分方程构造的模型不是唯一的，作者构造了另一种指数序列模型，我们称之为灰色指数模型(GEM)，它可以代替GM(1,1)模型对灰色系统进行预测。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Grey System 数学-数学跨学科应用

CiteScore

2.40

自引率

43.80%

发文量

审稿时长

1.5 months

期刊介绍： The journal is a forum of the highest professional quality for both scientists and practitioners to exchange ideas and publish new discoveries on a vast array of topics and issues in grey system. It aims to bring forth anything from either innovative to known theories or practical applications in grey system. It provides everyone opportunities to present, criticize, and discuss their findings and ideas with others. A number of areas of particular interest (but not limited) are listed as follows: Grey mathematics- Generator of Grey Sequences- Grey Incidence Analysis Models- Grey Clustering Evaluation Models- Grey Prediction Models- Grey Decision Making Models- Grey Programming Models- Grey Input and Output Models- Grey Control- Grey Game- Practical Applications.