Criterions of comparing two function transformations with the same monotonicity to raise the second class smooth degree

Abstract-Criterions of comparing two function transformations with the same monotonicity to raise the second class smooth degree is presented in this paper, and we prove the transformation F(a_k) =a_k/d_o^k-1 only changes the first class smooth degree of the data series, but can´t change the second class smooth degree of the data series. That is, the effective measures for the first class gray forecasting model to raise the forecasting accuracy may no longer be effective for second class gray forecasting model.