An Unequal Interval GM(1,1) Model Based on the Modified Initial Value and Its Equivalence Model
He Xia · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2011
In this paper,by letting initial value of unequal interval GM(1,1) model which whitenization differential equation was dx(1)(t)dt+ax(1)(t)=u x(1)(k1)=x(0)(k1) have modified initial value x(0)(k1)+β,the new unequal interval GM(1,1) model which whitenization differential equation was dx(1)(t)dt+ax(1)(t)=u x(1)(k1)=x(0)(k1)+β is put forward,and naturally,the form of unequal interval GM(1,1) model is extended.Then,we proved the equivalence of the new unequal interval GM(1,1) model and an unequal interval GM(1,1) model based on the initial value αx(0)(k1).Lastly,a applied example shows that this model in this paper has effectiveness and practicability.These results not only revealed an essential connection existed between the two unequal interval GM(1,1) models,but also provided the greater choosing space with application of unequal interval GM(1,1) model.