GM (1, 1) Model based on the transformation of function [1/(a − e− bx )]

In this paper, the grey model (GM) based on the function 1/a-e^-bx transformation is proposed. It is proved theoretically that function 1/a-e^-bx transformation can prevent discrete series from changing rapidly so as to satisfy with GM conditions, and the series after being transformed by 1/a-e^-bx has better smooth degree than those by logarithm function being transformed. The GM precision based on 1/a-e^-bx is improved greatly. The method is especially suit for modeling series that changes fast, and it can expand the range of GM application wildly. Finally the method is applied in building the model of average wage of staff and workers in China and the results show the effectiveness of the approach.