基于逐步优化构造背景值和倒数累加生成非等间距多变量的优化MGRM(1,n)模型

The non-equidistant multi-variable optimizing MGRM(1,n) model based on a step by step optimum constructing background value and accumulated generating operation of reciprocal number

灰色系统理论是研究贫乏信息的科学理论,具有广泛的适应性.应用逐步优化的建模方法构造多变量非等间距优化灰色模型MGRM(1,n)的背景值,以相对误差均值最小为目标函数,以MGRM(1,n)响应初值修正量为设计变量,基于倒数累加生成建立了非等间距多变量优化灰色模型MGRM(1,n).该模型不仅适合于等间距建模型,也适合于非等间距建模,拓广了灰色模型的应用范围.该模型精度高,使用简单.实例表明所建模型的实用性与可靠性.

Grey system is a theory which studies poor information specially, and it possesses wide suitability. Applying a step by step optimum modeling method, constructing background value of non-equidistance multi-variable optimizing Grey model MGRM（1, n）, taking the mean relative error as objective function and taking the modified values of response function initial values as design variables, based on accumulated generating operation of reciprocal number non-equidistance multi-variable optimizing Grey model MGRM（1, n） was built. The proposed model can be used to build model in non-equal interval ＆ equal interval time series, enlarges the scope of application, and, has high precision and easy to use. Example validates the practicability and reliability of the proposed model.