初值修正灰色GM(1,1)模型的等价性

Equivalence of Grey GM(1,1) Models Based on Modified Initial Value

研究了初值修正灰色GM(1,1)模型的等价性问题.通过选取两个不同初始条件x(1)(1)+β1、β2 x(1)(1),分别得到两个初值修正GM(1,1)模型,并证明了它们的等价性;然后,推广初值修正GM(1,1)模型等价性,得到了结论更为一般的、初值条件为x(1)(i)+β1和β2 x(1)(i)的、两类GM(1,1)模型的等价性.这些结论不仅揭示了不同初值条件的GM(1,1)模型的本质联系,而且为进一步应用GM(1,1)模型提供了更大的选择空间.

We have studied the equivalence of grey GM（1,1） models based on modified initial values. Letting respectively modified form x（1）（1）＋ β1,β2x（1） be the initial condition, the two optimized GM（1, 1） models were put forward, and the equivalence of the two optimized GM（1, 1）models was proved in this paper. Then, by generalizing the equivalence of GM（1, 1） based on modified initial values, the equivalence is generalized to the equivalence of two class optimized GM（1,1） models based on x（1）（i）＋β1, β2x（1）（i）. These results not only revealed a essential connection existed between the two class of GM（1,1） models based on different modified initial values, but also provided the greater choosing space with application of GM（1,1） models.