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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) mode! 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. [ABSTRACT FROM AUTHOR]

In this paper, a forecasting method for the fluctuating interval number series is proposed. Firstly, the definition equation of GM (1, 1) is improved to suit the interval number series directly and the interval number series needs not to be transformed into real number series. The development coefficient of the definition equation is taken as an accurate number, but the grey input of the definition equation is taken as an interval number. By this method, the binary interval GM (1, 1) (BINGM (1, 1)) is proposed. In order to further make the model fitting to the fluctuating inten'al number series, the support vector machine (SVM) is introduced to amend the predicted results of BINGM (1, 1) and SVMBINGM (1, 1) is proposed. In the process of amendment, the inten'al series is transformed firstly to avoid the disorder of the boundary points of the interval series. The results of the application example show that the prediction accuracy of SVMBINGM (1, 1) is higher than BINGM (1, 1) for the forecasting of fluctuating inten'al series. [ABSTRACT FROM AUTHOR]