Grey system theory is widely used to deal with the uncertainty caused by partially known information. Grey time series analysis plays an important role in decision-making and forecasting, of which grey forecasting is the key branch. The traditional grey multivariable model is limited to be widely used in practical application because of its lack of prediction accuracy and poor adaptability. Kernel Methods is a powerful pattern recognition algorithm in machine learning, which is particularly good at dealing with nonlinear multivariable models. A novel nonlinear conformable fractional accumulation kernel grey GM (1, N) model on account of the kernel method (abbreviated as CFAKGM (1, N)) is arranged in this work to improve the prediction accuracy. Furthermore, the utilization of conformable fractional accumulation enhances the prediction accuracy of the model, and the model's hyperparameters are determined through the application of the four vectors intelligent metaheuristic method (abbreviated as FVIM). Numerical investigations demonstrate that when processing the prediction of complex systems, the CFAKGM (1, N) model may capture the nonlinear dynamic properties of the data more effectively and enhance the prediction accuracy significantly.

Shaoyong Liu. Research on a novel nonlinear conformable fractional accumulation kernel GM (1, N) model. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 3: 147-157. https://doi.org/10.25236/AJMS.2024.050317.

[1] Zhang D, Luo D. Research on the prediction model of agricultural drought hazard considering the time-delayed cumulative effect and system development characteristics [J]. Science of The Total Environment, 2023, 882: 163523.

[2] Sapnken F E, Ahmat K A, Boukar M, et al. Forecasting petroleum products consumption in Cameroon's household sector using a sequential GMC (1, n) model optimized by genetic algorithms[J]. Heliyon, 2022, 8(12).

[3] Meng Z, Liu X, Yin K, et al. Forecasting China's energy intensity by using an improved DVCGM (1, N) model considering the hysteresis effect[J]. Grey Systems: Theory and Application, 2021, 11(3): 372-393.

[4] Guo X, Wu L, Wang M. Application of Grey Lotka-Volterra model in water-economy-industry-technology innovation system in Beijing-Tianjin-Hebei region[J]. International Journal of Environmental Research and Public Health, 2022, 19(15): 8969. 

[5] Ma X, Liu Z. The kernel-based nonlinear multivariate grey model[J]. Applied Mathematical Modelling, 2018, 56: 217-238.

[6] Khalil Roshdi, Al Horani M, Yousef Abdelrahman, Sababheh Mohammad. A new definition of fractional derivative[J]. Comput Appl Math 2014; 264: 65–70.

[7] Xie M, Wu L, Li B, et al. A novel hybrid multivariate nonlinear grey model for forecasting the traffic-related emissions[J]. Applied Mathematical Modelling, 2020, 77: 1242-1254.

[8] Hou H, Xu P, Zhou Z, et al. Hardware error correction for MZI-based matrix computation[J]. Micromachines, 2023, 14(5): 955.

[9] Verma S, Boonsanong V, Hoang M, et al. Counterfactual explanations and algorithmic recourses for machine learning: A review [J]. ACM Computing Surveys, 2020. 

[10] Ma X, Wu W, Zeng B, et al. The conformable fractional grey system model[J]. ISA transactions, 2020, 96: 255-271.