基于函数x^(-a)变换的GM(1,1)模型及在我国农村人均住房面积建模中的应用  

GM(1,1) Model Based on Power Function x^(-a) Transformation and Its Application in Chinese Country Per-capita Housing Areas Modeling

作　　者：戴文战[1] 李俊峰[1] 

机构地区：[1]浙江理工大学自动化系

出　　处：《系统工程理论与实践》2004年第11期63-67,共5页Systems Engineering-Theory & Practice

基　　金：浙江省自然科学基金(602016)

摘　　要：　提出了对建模数据进行幂函数x-a(a>0)变换,理论上证明这种变换可以有效地提高建模数据序列的光滑度和所建GM(1,1)模型的精度,而且其模型精度优于对数变换所建模型,从而大大拓宽了灰色模型的应用范围.用文中所提方法建立了我国农村人均住房面积的模型,实例表明了该方法的有效性.In this paper, the method of power function x^(-a)(a>0) transformation against modeling data is put forward. It has been proved that the smooth degree of discrete data after this transformation can be enhanced. Moreover, the GM(1,1) model precision based on the data transformation is better than the model precision based on logarithm function transformation. So the method can widen range of application of grey model. At last, the model of Chinese country per-capita housing areas is built by means of the method. The practical application shows the effectiveness of the proposed approach.

关 键 词：灰色模型 光滑度 建数据序列 幂函数变换 

分 类 号：N941.5[自然科学总论—系统科学]