分数阶GM(1,1)生成算子公式证明及其模型构建

Formula Proofs of Fractional Order GM(1,1)AGO and Its Model Build

为了改进预测精度,GM(1,1)模型已被拓展到分数领域.指出在现有文献中,分数阶累加生成算子和逆累加生成算子公式证明存在瑕疵,因为它从整数角度证明的公式然后应用到分数领域中.因此,严格从分数角度出发,证明了分数阶累加生成算子和分数阶逆累加生成算子公式,并构建了FGM(1,1)模型.

GM(1,1)model with the fractional order accumulation is proposed for improving prediction accuracy.This paper points out that it is incorrect the formula proofs of fractional order AGO and IAGO under the view of integer in the literatures.So under the view of fraction,the formulas of are proved again and the model of fractional order is rebuilt in this paper.