Abstract: Multivariate grey models are commonly used to evaluate the independent effects of related factors, but they may fail to account for any nonlinear interactions that could exist between them. To address this limitation, this study introduces the INDGM(1,N) model, which considers the nonlinear interactions between related factors. Simultaneously, to depict the nonlinear impact of both the system behavior sequence and corresponding factor sequences more accurately, varying power parameters have been incorporated into the model proposed in this paper. Moreover, by adjusting the parameter values of the INDGM(1,N) model, it can be converted into several other models, such as the DGM(1,N) model, GM(1,N) model, DGM(1,1) model, or GM(1,1) model. This study uses a genetic algorithm to obtain the time response of the INDGM(1,N) model by solving its nonlinear characteristic parameters. We then use the model to simulate and forecast China's CO2 emissions and compare its performance with that of other models. The results show that the INDGM(1,N) model provides more accurate simulation and prediction accuracy than other models, highlighting its effectiveness. 

Key words: Grey prediction model, INDGM(1,N) model, Interaction, Genetic algorithm