函数变换对灰色模型光滑度和精度的影响  

Effect on grey model's smoothness and accuracy by using function transformation

作　　者：郭金海[1,2] 肖新平[1] 杨锦伟[1,3] 

机构地区：[1]武汉理工大学理学院,武汉430070 [2]长江大学信息与数学学院,湖北荆州434023 [3]平顶山学院数学学院,河南平顶山467000

出　　处：《控制与决策》2015年第7期1251-1256,共6页Control and Decision

基　　金：国家自然科学基金项目(51479151);高校博士点基金项目(20120143110001);教育发展社科基金项目(11YJC630155);湖北省青年基金项目(Q20121203)

摘　　要：对于单调序列的函数变换,首先将单调递增和递减函数变换提高序列光滑度的充要条件统一,给出压缩变换满足的充要条件,并给出还原误差精度提高的充要条件,得到提高光滑度与压缩变换的条件是一致的,但与降低还原误差的条件是矛盾的结论.由此,在函数变换时要综合考虑光滑度和还原精度,使得总体建模精度达到最优.最后通过文献中的结果进一步表明了所得到结论的正确性.In view of the function transformation to monotone sequence, the sufficient and necessary conditions of monotonic increasing and decreasing function transform are unified to improve the smoothness of the series. The sufficient and necessary conditions which compression transform meets are given, and the necessary and sufficient conditions of reduction the accuracy of error are also given. A conclusion is obtained that the conditions of improving the smoothness and compression transform are consistent, but are contradictory with that of lowering the reduction error. Therefore, the smoothness and reduction accuracy are considered comprehensively during the function transformation to achieve the optimal overall modeling accuracy. Finally, the literature results show the correctness of the proposed conclusion.

关 键 词：灰色模型 光滑度 函数变换 建模精度 还原误差 

分 类 号：N941.5[自然科学总论—系统科学]