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ISBN 978-952-5726-09-1 (Print)
Proceedings of the Second International Symposium on Networking and Network Security (ISNNS ’10)
Jinggangshan, P. R. China, 2-4, April. 2010, pp. 073-076
Improving Prediction Of Model Gm (1, 1) Based
On Class Ratio Modeling Method
Qin Wan 1 , Yong Wei 2 , and Shuang Yang 3
1 College of Mathematics and Information,
China West Normal University, NanChong, SiChuan, 637009, China
2 College of Mathematics and Information,
China West Normal University, NanChong, SiChuan, 637009, China
3 College of Mathematics and Information,
China West Normal University, NanChong, SiChuan, 637009, China
wanqin1014@126.com, 3306866@163.com,yangshuang_cwnu@163.com
Abstract—This article introduces a new method of how to
find suitable class ratio according to the class ratio
modeling method thought. It causes the class ratio modeling
method to be used on the non-steady primitive sequence
which has non-homogeneous grey index law directly. And it
both extends the application scope of the class ratio
modeling method, and avoids the tedious data pretreatment
process effectively while improving prediction precision of
model GM (1, 1).
Index Terms — Class ratio modeling , GM (1,
1) ,Weakening , Buffer operator
I. INTRODUCTION
Since Mr. Deng Julong has proposed the grey system
theory, the application of grey model spreads many
domains. Grey model has more advantages compared to
traditional prediction method because that grey model
has the characteristics of few sample data required, easy
calculation, and high prediction accuracy in short terms
etc. However in practical application, people discovered
that model GM (1, 1) is suitable for slowly increasing
data, but its fitting effect with quickly increasing data is
unsatisfactory. Professor Liu Sifeng had theoretically
proven that the applicable scope of development
coefficient a is limited to ( − 2 , 2 ) , and the effective
range of it is narrower [ 1]
. Therefore, many scholars have
made improvement and optimization on grey model from
different angles. For instance, many references expand
the applicable scope of development coefficient a by
reconstructing background value or optimizing grey
derivative to improve simulating and predicting precision
of grey model, and achieve good results.
Because the process of obtaining a by solving grey
differential equation is just making whitenization
estimation on a,the author in reference [2] puts forward
class ratio modeling method of single consequence in
[Key research projects] A project supported by scientific research fund
of Sichuan Education Department.(2006A007) and basic application
research fund of Sichuan (2008JY0112).,and a project supported by
china west normal university item(08B032).
Wan Qin: teaching assistant of College of Mathematics and
Information , China West Normal University. major study is Grey
System Analysis. Tel:18990874811. E-mail: wanqin1014@126.com
grey system based on this idea.The primary data
sequence is not suitable for establishing grey model
directly if it could not pass feasibility test, so we can
make data preprocessing such as carrying buffer
[3]
operator on the primitive behavior data sequence
before establishing model GM(1,1) on it. Reference [4]
propose using weakening buffer operator to affect the
primitive behavior data sequence which possesses
characteristics: the front part grows (weakens)
excessively quickly and the latter part grows (weakens)
excessively slowly; Reference [5] propose using
strengthening buffer operator to affect to the primitive
behavior data sequence which has subsequent
characteristics: the front part grows (weakens)
excessively slowly and the latter part grows (weakens)
excessively quickly. Buffer operators can effectively
eliminates the disturbance affect to the primary data
effectively in the modeling and forecasting process, and
improve the predicting precision of model GM (1, 1). For
primary data sequence which has above characteristic,
this paper introduces a new method of how to find
suitable class ratio according to the class ratio modeling
method thought. It causes the class ratio modeling
method to be used on the non-steady primitive sequence
which has non-homogeneous grey index law directly.
And it both extends the application scope of the class
ratio modeling method, and avoids the tedious data
pretreatment process effectively while improving
prediction precision of model GM (1, 1).
II.
SUMMARY OF THE CLASS RATIO MODELING
METHOD
[2]
Definition As for monotone sequence
X = { x(
k ) x(
k ) > 0, orx ( k ) < 0, k = 1,2,3.... n}
,then
x(
k −1)
σ ( k)
= , k ∈ K = { 2,3,... n}
is called the back
x(
k)
class ratio (hereinafter using class ratio) at k point of
X , and x(
k )
τ ( k ) = , k ∈ K = { 2,3,... n}
is called
x(
k − 1)
the front class ratio at k point of X .Obviously, the back
class ratio and the front class ratio both are the reciprocal
value of each other, and both are positive numbers.
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