灰色预测GM(1,1)模型的一点改进

讨论了灰色预测GM(1,1)模型理论上存在的一些问题,认为在解微分方程dXdt(1)+aX(1)=b进行预测公式推导时,把-X1(1)=X11作为已知条件来确定微分方程的解是不合理的,而应根据实际情况,不局限于{X(1)(k)}序列,直接从最后的平均相对误差ε-=n1∑k=n1ε(k)入手,将-ε看作是常数cm的函数,求出满足Min{-ε(cm)}的cm值即可,并在此基础上推导出cm的计算公式,形成新的灰色预测公式,从而进一步提高预测精度,最后经过实例验证新的预测公式的正确性及可行性.

Improvement of Grey Prediction Model GM(1, 1)

This paper discusses some problems of the grey predication model of GM(1,1) exsiting,and points out that in the solution differential equation dX~(1)dt+aX~(1)=b,it is unreasonable that ~((1))(1)=X~(1)(1) is looked as the known condition to deduce the predication formula in order to calculate the differential equation′s solution.Instead,according to truth,the known condition should not be limited to the {X~(1)(k)},and the last average and opposite mistake(=1n∑nk=1 εk) is directly considered,being regarded as the c_m′s function.At last,the value of c_m is calculated to make the value of be the minimum.Based on it,the c_m′s formula is conducted,and the new grey prediction formula is formed to improve predication accuracy.Finally,the illustration is used to verify accuracy and feasibility of the predication formula.