In general, there are different types of uncertain systems with small samples and poor information in the real world. The grey system is a system with partially known (white) and partially unknown (black) information. Grey models play an important role in modeling, prediction, evaluation, decision making, control and system analysis in many fields because of their simple expression and computation, and excellent prediction performance with insufficient data.
GM(1, 1) model is an important part of the grey model, where ‘GM’ stands for ‘grey model’ while the first number ‘1’ in brackets indicates the first order differential equation and the second number ‘1’ indicates the differential equation of one variable. It is mathematically based on the first order linear ordinary differential equation and least square method. It requires a relatively small amount of data (four or more samples) to develop a mathematical model, and a simple calculation process to analyze the behavior of an unknown system. It has been widely used because it does not require a large number of samples and has low computational complexity and there is no limitation of statistical assumptions.
Up to now, many research works to improve the accuracy of the GM(1, 1) have been carried out on the following aspects. Most of them have used mean absolute error (MAE), mean absolute percentage error (MAPE), mean squared error (MSE) and root mean squared error (RMSE). The accuracy measures are calculated using the arithmetic average operation of errors at the fitting points, and they include no sufficient information about prediction accuracy. Consequently, most of the previous works may be regarded as the works for improving the fitting accuracy of the GM(1, 1). It may be a common drawback of the previous works for improving the performance of the GM(1, 1).
Yang Won Chol, a researcher at the Faculty of Materials Science and Technology, has proposed an improved GM(1, 1) model based on weighted mean squared error (MSE) and optimal weighted background value: OB-WMSE-GM(1, 1). He applied it to one simulation example and two application examples to verify its effectiveness.
In the simulations and applications, the errors for GM(1, 1) were much smaller than conventional GM(1, 1).
You can find the details in his paper “An improved GM(1, 1) model based on weighted MSE and optimal weighted background value and its application” in “Scientific Reports” (SCI).
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