Study On The Relationship Between Background Value And Accuracy In GM(1,1,α)Model

As one of uncertainty theories, grey system has been set up the structure theory system which contains system analysis, optimization, control, modeling, decision-making, evaluation and forecasting technology. GM(1,1,a) model is an important part of the grey system theory, it has used in many fields, so it has an extremely important practical significance on researching influence to model accuracy by expanded forms and background value’s change of the GM(1,1,a) model. This paper mainly studies this problem. This paper’s main work includes three aspects as follows:(1)This article researches the various expanded forms of GM(1,1, a) model, then acquiring five kinds of derivative model of grey model. On the theoretical basis of study about the derivative model of grey GM(1,1,a) model, we discuss the parameters restricted zone of model and deduce the value range of development coefficient and grey action.(2)Through establishing secondary parameter bag of grey model and using the method of eliminating intermediate parameters of grey model, we can deduce the expressions among background value, development coefficient and grey action. Then research the influence on development coefficient of grey model by changing the background value and obtain the relationship between them. The results show that there is a monotone relationship (monotone increasing or monotone decreasing) between the development coefficient and parameters of background value.(3) This paper further studies the influence on grey model’s error by changing the background value. Then it has the result that we can control the grey model’s error through adjusting the background value. Firstly we deduce the expression between parameters of background value and model predict value and get the relational expression between parameters of background value and model’s residual, relative error. Then we analyze the background value’s change which has influenced the model errors by using the nature of the composite function. The result is that there is a monotone relationship between models error and parameters of background value when it meets certain conditions.