GM(1,1)模型中背景值的优化

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.200709.0002

Zhengxin Wang, Yao-guo Dang, Sifeng Liu, Jing Zhou

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引用次数: 25

摘要

本文证明了具有非齐次指数律的离散函数是由具有齐次指数律的离散函数累加得到的，而具有齐次指数律的离散函数是由具有非齐次指数律的离散函数反累加得到的。在分析GM(1,1)模型误差的基础上，利用非齐次指数律离散函数拟合累积序列，提出了GM(1,1)模型背景值优化的新方法。将最优模型与GM模型进行仿真对比，表明新模型突破了自适应系数的限制，并提高了模型的匹配精度和预测精度。

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The Optimization of Background Value in GM(1,1) Model

In this paper, we prove that discrete function with non-homogeneous exponential law is generated by accumulating the discrete function with homogeneous exponential law while discrete function with homogeneous exponential law is generated by inversely-accumulating the discrete function with non-homogeneous exponential law. Based on the error analysis of the Model GM(1,1), we use the discrete function with non-homogeneous exponential law to fit the accumulated sequence in order to propose a new method for optimizing background value in Model GM(1,1). By contrasting the optimum model to the GM one with the simulation, it can be concluded that the new model broke through the restricts of adaption coefficient and it still improved its matching and prediction precision.

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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.