Improvement of GM(1 , 1)Modeling Accuracy Based on Function Transformation

In order to expand the scope of application of the GM(1,1) model, by introduction of function transformation to improve the modeling accuracy has been a general practice. However, it is found that many functions can greatly improve the modeling accuracy yet there is also a too large reduction error. Through an in-depth analysis of F(x(s)) = x(s)/ (s+C)α(α>0) , it is pointed out that the said function transformation can actually increase the modelling accuracy and then the appli- cation scope of the parameterα, namely,α∈ R Then two simple methods for determining the parameters C,α are provided, which perfectly rids the disadvantages of blind determining of the initial values. By use of the function transformation and the method of parameter determining, the accuracy of GM(1,1) modeling is markedly improved, which proves the feasibility of the improved method. Lastly, the author points out the wrong cognition that the higher the smoothness is, the higher the modeling accuracy. It also has to take into account the approximate equality for the modeling sequence.