Data Transformation Technology To Improve Modeling Accuracy Of Grey System Method

Grey system theory founded in 1982 by Chinese scholar Deng Ju-long, which is a new methods to research the uncertain problem that is "part of the information is known, some information is unknown”. As one of the core content of the theory of grey system, GM(1,1) model has been widely used in many fields such as society,economy, science and technology, industry and agriculture, its value has been gradually recognized. But the scope of the traditional GM(1,1) model is low growth and nearly exponential sequence, most sequence in reality is neither a low growth sequences nor nearly exponential sequence, so people tried to transform the original data through the data transformation technology then modeling,to achieve the purpose of improving the modeling effect.Firstly, this paper discusses the necessary condition of the relative error between the inverse transformed function transformation sequence and original sequence, is not larger than the relative error between the transformed sequence and its corresponding simulation. And points out the necessary condition of the inverse transformation and no enlarged relative error’s necessary conditions for both monotone increasing and monotone decreasing function transformation respectively. Meanwhile, according to the actual example shows that the condition is not sufficient, as a particular case application it obtains the necessary conditions of general discrete transformation after inverse transformation the relative error not enlarged. And proves monotone increasing and monotone decreasing function transformation respectively that the function transformation does not exist which both improve the data smoothness or reduce class ratio dispersion and keep the relative error not enlarged after inverse transformation.Secondly, according to the basic fact that the traditional prediction model is suitable to low growth and approximate exponential sequence, put forward that using the class ratio dispersion of the original sequence its own to compare the degree of low growth, using the class ratio dispersion of the class ratio sequence to compare the degree of the original sequence is close to the exponential sequence. Then give the example that is more smooth but lower approximate exponential degree, which cause lower modeling precision, obviously it shows that approximate exponential is a significant condition. And give two methods of data transformation can improve modeling precision which according to smoothness and class ratio dispersion respectively.Thirdly, this paper proposes a definition that one of two sequences is closer to the low growth and approximate exponential sequence. And combine the method that data transformation can improve the modeling accuracy which presented in this paper, find a kind of series function transformation f_k(x(k))=x(k)/d~k,d= >, the condition of series function transformation can improve modeling precision is d∈(1,m] ((M,1]) for monotone increasing( decreasing) sequence, And the condition of can reduce modeling precision is d∈[M,+oo) ((0,M]),the condition of which both may improve mode the condition of which both may improve modeling precision and reduce modeling precision is d∈(m,M). m 、 M are the minimum or maximum value of the class ratio sequence after each square.At last, this paper shows the feasibility and correctness of the conclusion in this paper by the examples, also shows the limitation of the traditional smoothness comparison principle and the traditional class ratio dispersion comparison principle,and show the reasonability of the new smoothness comparison principle and the new class ratio dispersion comparison principle at the same time.