Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

近似非齐次指数增长序列的间接DGM(1,1)模型分析

DGM(1,1)模型对近似齐次指数增长序列具有较高的预测精度,而实际上服从近似齐次指数增长规律的数据序列十分有限。根据灰色系统理论的差异信息原理,通过原始序列的累减生成将近似非齐次指数增长序列转化为近似齐次指数增长序列,对累减生成序列建立DGM(1,1)模型,并在此基础上实现对原始序列的还原以达到数据模拟及预测之目的。因原始序列的累减生成最大可能地满足了建模序列的齐次性要求,提高了模拟及预测精度,拓展了模型的适用范围,故通过算例验证了此种改进方法的简单性、实用性及有效性。

近似非齐次指数递增序列的IANGM(1,1,k)模型构造

针对具有近似非齐次指数规律的递增序列,文章提出利用原始序列与其对应的一次累减生成序列来构建更符合近似非齐次指数规律的新模型IANGM(1,1,k),模型中白化方程的解恰能表示为关于原始序列的时间响应式,使得模型不再需要累减还原过程就能直接进行模拟和预测,简化了建模过程,并从理论上证明了IANGM(1,1,k)模型中的累减生成序列是非负的近似非齐次指数序列,最后通过实例验证了新模型具有较高的模拟预测精度及实用性。