Study On The Stability And The Modeling Precision Of Grey Model

Grey system theory studies the uncertain systems that partial information is known, and others are unknown. Through more than twenty years' development, this theory is more and more perfect and mature, and it has established one booming subject of plot structure. It is applied in many fields now. Especially, the stability and the precision problem of grey prediction model are the research hotspots in the grey system theory all the time, and many scholars research them. On the one hand, solving the stability problem is the premise of using grey prediction model; on the other hand, the grey model will be widely applied if we improve the precision and reduce the error of grey prediction model. In this paper, we mainly research the stability and the precision of grey prediction model. Firstly, we discuss the stability problem that the precision of model sometimes is high and sometimes is small (that is the stability problem of solution); secondly, we discuss the influence factors of multiple transformation on the precision of models; finally, this paper takes the example of non-equigap GM(1,1) model, and researches the stability problem (namely ill-conditioned problem) and properties of non-equigap model.The grey prediction model is established on the basic of the theory that the original sequence will present obvious exponential law after the accumulated generating operation. And it is based on the accumulated generating operation and the least square method. But it produces error frequently when it is used to fit the pure exponential sequence. By contraries, the fitted curve of a raw series which has big fluctuation and has no exponential law will be an exponential curve after GM(1,1) modeling. This is the stability problem of the predictive solution of the grey model. This paper makes a deep study on the definition form and connotation of GM(1,1) model, and analyses the reasons of stability problem in the model and gives the theoretical proof. Moreover, a pure exponential sequence is fitted.Many scholars point out the misunderstanding which we thought all the time that the data transformation can improve the precision of model effectively only if it can improve the smooth degree of original sequence. Based on it, the paper explores some main influence factors of data transformation on the precision of model, i.e. the smooth ratio, the class ratio and the convex and cave of original sequences. It extends the application of data processing technology. In the meantime, this paper discusses the effect difference and the applied condition of some common data transformations. It has some instructional meaning and referenced value in practice.The data processing technology is also the main tool for discussing the ill-conditioned problem of non-equip GM(1,1) model in this paper. The paper...