灰色模型的最优化及其参数的直接求法

The Optimization of GM(1,1) Model and a Method of Solving the Parameter

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.

This article proposed a method which does not need to solve the AGO series or the average value and does not involve the concept of grey differential equation and the general differential equation can solve the grey model parameter α,c directly, the new model which established by this method is the optimized model, because it not only satisfies the least sum of squares of the simulation absolute error （or least sum of squares of simulation relative error）or the precision condition theoretically, but also has the white exponential law coincidence property and white coefficient law coincidence property and stretching uniformity property. Finally the operation of this method is confirmed by the example. Both the simulation precision and the effect are better.