The error analysis in GM(1,1) model via fractional power of grey generating

The GM(1,1) model in the grey system theory is a prediction model. It aims to construct the first differential model, which uses the background value of two adjacent points. In the previous researches, they found that the most important factor which had great impact on prediction error was background value. Hence, many researches focus on background value adjustment, including alpha value's digital jumping changes or the alpha value's continuous changes. However, even in this form, it sometimes still fails to present discrete points' implied law which result in the impossibility of lowering GM(1,1) errors. Therefore, the paper proposed a new method, including three major elements. First, the background values were presented in fractional power type and combine with consist method as the basic to get the real value for reduce the prediction errors. Next, the GM(1,1) model was integrated, and developed a prediction error reduction method. As the result, the paper not only can got rid of the traditional background value method, but also created a new research direction of using GM(1,1) model to reduce prediction errors.