Uncertainty Weakening of GM(1,1) Model

In the real world, the observations or statistical data are known as white numbers, but they are grey which means that they deviate from the true values because of disturbances and errors. And this paper applied random simulations to reveal that GM(1,1) model can weaken these disturbances or uncertainty. The exponential sequences with different development coefficients and random disturbances are generated randomly, and the sequences are used for GM(1,1) modeling, and then the mean absolute percentage errors (MAPEs) of the modeling are compared and analyzed. It is found that the MAPEs between fitted values and real values are smaller than those between the original values and real values, which shows that GM(1,1) model can weaken uncertainty.