The Construction of a New Kind of Weakening Buffer Operators

Through optimizing the existing weakening buffer operator and introducing then m as parameter, this paper constructs a kind of weakening buffer operator, which improved the prediction accuracy; and verified by an example, the effect tis good


Introduction
Established by Mr. Deng Ju-long since the 1980s, the grey system theory has been widely applied in the industry, the agriculture, the economy, the building and so on.The grey system theory through the original data on social, economic, ecological system of mining and finishing to seek its regularity, which is a kind theory system to find the data law from the original data.Both of the experimental data or the statistical data, the data must be analyzed before modeling, otherwise there will be a quantitative analysis of the forecast results and qualitative conclusion does not match, the cause of the problem lies not the model, but because the system behavior data has been shocked.So, find the combine point of quantitative prediction and qualitative analysis, exclude the impulse interference, restore the data true colors, improve the prediction accuracy, that are the most important work.The grey system theory through the original data on social, economic, ecological system of mining and finishing to seek its regularity, which is a kind theory system to find the data law from the data.But using several kinds of weakening operators to process all data which have different change rules, sometimes the effect meets not ideally.When faced the data which have a sharp change from high growth to low-growth, for reaching the high accuracy, it is necessary to process the data by using the high-end weakening buffer operator, the process of treatment is cumbersome.When the prediction data are smaller than the real data by using the first-order weakening buffer operator, and the prediction accuracy is not ideally, if continue to use the high-end weakening buffer operator, the forecasting result will be possibly smaller, the prediction error will further enlarge .
Through optimizing the existing weakening buffer operator and introducing then m as parameter, This paper constructs a kind of buffer operator, which improved the prediction accuracy; and verified by an example, the effect tis good

The Existing Buffer Operators
Satisfies the following condition the operator we to call it the buffer operator: Let X be a system behavior data series, (1) D is the operator affect to X, and the operator D satisfies x(n)d=x(n).(2) Each data x(k), k=1, 2, …, n in X should participate fully in the entire process of operator function.(3) Arbitrary x(k)d, k=1, 2, …, n can be expressed by a unity primary analytical expression.(The above three conditions are called three axiom of buffer operators).

XD XD 
, then 3 D is the average strengthening buffer operator (ASBO).4 D is the geometric average strengthening buffer operator (GASBO).Definition 2 If ( (1), ( 2), ( )) X x x x n  is a system behavior data series, the weight vector of each point is 1) , ( 2) , ( ) ), 5,6 Then D 5 is the weighted average weakening buffer operator (WAWBO), D 6 is the weighted geometric average weakening buffer operator (WGAWBO).Especially when is the average weakening buffer operator (AWBO).D 8 is the geometric average weakening buffer operator (GAWBO).

The Construction of Weakening Buffer Series and Their Characteristics
x n  is a non-negative monotone increasing series, that means 0 (1) ( ) So D is a weakening buffer operator.
Characteristic Weakening buffer series XD and system behavior data series X have the same monotonicity.
And X is a non-negative monotone increasing series, 2) By the same methods show, if X is a non-negative monotone decreasing series, XD is also a non-negative monotone decreasing series.

Example Analysis
Some city industry total output value (1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991) (Unit: billion) is (1786.3 2585 2993.8 3574 4590.3 5448.4 5888.4 6632.3)Takes the modeling data by 1984-1989 years data, and takes the simulation examination data by 1990 and 1991 data.From the raw data, we can find that the tertiary industry total output value average growth rate is 25.4% from 1984 to 1989.Analyzes it, the main reason is in the initial period of reform and opening, our government has made a series of preferential policy to support the development of industries.After ten remaining years' development, our country economic obtains the big development.As the support from country become weakening and the influence of domestic and foreign political configuration, economic situation, this kind of development speed is unable maintains.If carrying on the forecast with this data, the result is difficult to be believed.To make the reasonable forecast to the tertiary industry total output value, the raw data series must be weakened.
Using the average weakening buffer operator (AWBO) D 7 and its second order buffer operator, the geometric weakening buffer operator (GAWBO) D 8 and its second order buffer operator and the method of this paper (Let 0.2 m  ) process the raw data, and get the weakening series data, which are: XD 7 : (3496.3 3838.3 4151.6 4537.5  From the tables, with the raw data series model to predict the effect is not very well, and the average error is nearly 16.5%.Establish models by XD 7 and XD 8 , the prediction accuracy has been substantial increased, however, the average errors are 4.5%、2.9%,they are still not very well.Especially, establish models by XD 7 D 7 and XD 8 D 8 , the prediction errors are further enlarge.But using the method in this paper, the average error is only 1.6﹪.This confirmed that the weakening buffer series of this paper have a certain practical value.

Conclusions
Through optimizing the existing weakening buffer operator and introducing then m as parameter, this paper constructed a kind of weakening buffer operator an confirmed that the weakening buffer operator is exist in

Table 1 .
And get the predictive value about 1990 and 1991, the result has shown in Tables: Predictive value and Effects

Table 2 .
Predictive value and Effects Finally through example, we can find the strengthening buffer operators are effectiveness and have its practical value.