A Novel Fractional Accumulative Grey Model with GA-PSO Optimizer and Its Application

The prediction of cyber security situation plays an important role in early warning against cyber security attacks. The first-order accumulative grey model has achieved remarkable results in many prediction scenarios. Since recent events have a greater impact on future decisions, new information should be given more weight. The disadvantage of first-order accumulative grey models is that with the first-order accumulative method, equal weight is given to the original data. In this paper, a fractional-order cumulative grey model (FAGM) is used to establish the prediction model, and an intelligent optimization algorithm known as particle swarm optimization (PSO) combined with a genetic algorithm (GA) is used to determine the optimal order. The model discussed in this paper is used for the prediction of Internet cyber security situations. The results of a comparison with the traditional grey model GM(1,1), the grey model GM(1,n), and the fractional discrete grey seasonal model FDGSM(1,1) show that our model is suitable for cases with insufficient data and irregular sample sizes, and the prediction accuracy and stability of the model are better than those of the other three models.