Combined Optimized SFGM(1,1,k) Model and Its Application in Total Import and Export

Since the introduction of the fractional FGM(1,1) model, it has been widely used in all aspects of society. However, the original FGM(1,1) model has certain defects. Therefore, many experts and scholars have proposed many optimization methods for the shortcomings of the fractional FGM(1,1) model, and have been well applied. Since the gray action of the FGM(1,1) model is a fixed constant, the dynamic variation characteristics of the system cannot be well described. Based on this, this paper proposes a new SFGM(1,1,k) model by optimizing the gray action amount and reconstructing the background value of the optimized model using Simpson formula to improve the FGM(1,1) model. Then, apply it to the numerical examples of import and export totals. The results show that the combined optimization of SFGM(1,1,k) has higher fitting accuracy and better prediction effect. The validity and practicability of the SFGM(1,1,k) model are verified. The application range of FGM(1,1) model is extended.