Download - Academy Publisher

Further
so
⎛ σ (1) ⎞
1 > ⎜ ⎟
⎝ σ ( n)
⎠
1
more
⎛ σ (1) ⎞
> ⎜ ⎟
⎝ σ ( n)
⎠
2
⎛ σ (1) ⎞
> ⎜ ⎟
⎝ σ ( n)
⎠
3
σ (1)
,
0 < < 1
σ ( n)
> ....... > 0
, namely
~
σ
would be more close to 1 if the value of t becomes
bigger.
2) When {()} x k is monotone decreasing about k ,
then the class ratio of each point x(
k − 1) ,
and letσ
( 1) = max{ σ ( k )} ≥ 1 , then,
σ ( k ) = ≥ 1
x(
k )
~
t
t
σ ( n)
− σ (1)
⎛ σ ( n)
n n
n n
t
⎟ ⎞
σ = σ ( ) + (1 − σ ( ))
= σ ( ) + (1 − σ ( )) 1 −
⎜
σ (1)
⎝ σ (1) ⎠
Further more
σ ( n ) ,
0 < < 1 σ (1)
so
1
⎛ σ ( n ) ⎞
1 > ⎜ ⎟
⎝ σ (1) ⎠
2
⎛ σ ( n)
⎞
> ⎜ ⎟
⎝ σ (1) ⎠
3
⎛ σ ( n)
⎞
> ⎜ ⎟
⎝ σ (1) ⎠
> ....... > 0
t
.
, namely
~
σ
would be more close to 1 if the value of t becomes
bigger.
End.
IV. EXAMPLE ANALYSIS
Take the data which is the industrial total output value of
a certain city in reference [6] as an example. Select the
industrial total output value of a certain city in 1997-
2004 as the primary
data,X=(187.85,303.79,394.13,498.27,580.43,640.21,702
.34,708.86)(Unit: Hundred million Yuan). Take the data
of 1997-2003 as the modeling data, and the data of 2004
as the inspection data.From the primary data, we can find
that the average annual growth rate of the industrial total
output value is 26.06% in 1997-2003years. Generally
speaking that it is impossible to maintain such growth
rate for a long time. So if we forecast with this data, the
result is difficult to believe. Through analyzing this
situation, we can find that because nation has given this
city some special industrial policies, thus the industry of
this city to obtain a very good development turning point.
But after 20 years, when the city's industry strength is
quite strong, the country will cancel the special policy.
So from now on, it is already impossible to maintain the
development speed as the same as before. In order to
make a reasonable forecast to development trend of this
city's industrial total output value, we can use weakening
buffer operator to eliminate the disturbance from the
special industrial policies on the later period industry
economy system development speed, and then enhance
the forecast precision of mode. In addition, we can
establish model on original sequence directly by
weakening class ratio modeling method.
Let us obtain model GM (1, 1) by weakening class ratio
modeling method and obtain model GM (1, 1) by using
the weakening buffer operator in reference [4] to
preprocess original data at first before establish model
GM (1, 1) respectively .
Next table 1 demonstrates the comparison among the
prediction precision of three kinds of models, the three
kinds of models are as follows: Establish model GM (1,
Prediction
Error
%1
1)based on the primary data without any data
pretreatment; Establishing model GM (1, 1) based on the
primary data after being made the second-order
weakening treatments by the weakening buffer operators
in reference [4];And establishing model GM (1, 1)based
on the primary data by weakening class ratio modeling
method which let t = 2,3,4, 5 respectively(the model
abbrevd respectively: Mod1、Mod2、Mod3、Mod4).
TABLE1 THE PREDICTION PRECISION COMPARISON AMONG THE
No
operator
AWBO
operator
GAWBO
operator
Mod1 Mod2 Mod3 Mod4
19.9 % 1.96 % 2.50 % 3.28% 1.89% 0.97 % 0.35%
ABOVE THREE KINDS OF MODEL
Note: The models GM (1, 1) based on no operator and buffer operator in reference[4]
are both original model GM (1, 1)
We can see from Table 1, If we do not deal with the
primary data by any means, establish GM(1,1) model
based on the primary data directly, then the prediction
error reaches as high as 19.9%;After making the secondorder
weakening treatments on the primary data by the
weakening buffer operators AWBO and GAWBO in
reference [4], the model prediction precision has been
enhanced greatly; And prediction precision of the model
GM (1, 1) established by weakening class ratio modeling
method is also improved effectively, the prediction error
can be smaller than 1%.
V. CONCLUSION
The weakening class ratio modeling method
introduced by this paper is practical and effective, and it
can be used on the non-steady primitive sequence which
has non-homogeneous grey index law directly. It has
simple calculation process, and does not involve some
grey system technical terms such as background value,
grey derivative, whitenization differential equation, and
it dose not involve some mathematical problem such as
solving inverse matrix etc. The weakening class ratio
modeling method 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).
REFERENCES
[1] Liu Sifeng Deng Julong. The Range Suitable for GM(1,1)
[J] System theory project and practice.2000(5):121-124
[2] Wang Yinao Pang Yangjun. Class ratio modeling method
of single consequence in grey system [J] Hebei coal
architectural engineering institute journal 1992(3):51-54
[3] Liu Sifeng. Forecast Trap of Impact Perturbation System
and the Buffer Operator [J] The academic journal of Huazhong
University of Technology, 1997,25 (1) 25-27
[4] Dang Yaoguo, Liu Sifeng, Liu Bin, Study on the
Weakening Buffer Operator [J] China management science
2004,12 (2): 108-111
[5] Xie Naiming, Liu Sifeng,.The Nature of the Strengthing
Buffer Operator and the Structure of the Structure of Certain
Practical Strengthening Buffer Operators.[J] Statistics and the
Decision-making 2006 (4) 9-10.
[6] China Bureau of Statistics, China Statistical Yearbook[Z]
Beijing: China Statistics Press, 1997-2005
76