| | Author | Model | Details |
| | Structural optimization | | Cui et al. [6] | NGM (1, 1, k, c) | A linear function is used instead of the constant as the grey action in the traditional grey model | | Qian et al. [7] | GM (1, 1, tα) | A grey prediction model with a power term with hyperparameter α as grey action | | Wei et al. [8] | GMP (1, 1, N) | A model is developed by using polynomial as the grey action of the grey model | | Liu et al. [9] | PTGM (1, 1, α) | Combination of GMP (1, 1, N) and GM (1, 1, tα) | | Saxena [10] | OFOPGM | A new data-driven grey prediction model using the time item with two hyperparameters as the action | | Wu et al. [11] | NGBM (1, 1, k, c) | A NGM (1, 1, k, c) model with nonlinear Bernoulli operators | | Liu et al. [12] | NGBM (1, 1, N) | A GMP (1, 1, N) model with nonlinear Bernoulli operators | | Ma and Liu [13] | TDPGM (1, 1) | A grey model with the function called time-delayed polynomial as the grey action | | Ma et al. [14] | FTDGM | A model is developed by using fractional time delayed term as the grey action of the grey model | | Xiang et al. [15] | HTGM (1, 1) | A prediction algorithm using hyperbolic time delayed polynomial as grey action | | Salehi and Dehnavi [16] | NGBM (1, 1) | Grey prediction model with the Bernoulli parameter | | Khan and Osinska [17] | ONGBM (1, 1) | A model that optimizes the background value of the model by using the integral mean value theorem |
| | Hybrid optimization | | Ofosu-Adarkwa et al. [3] | Verhulst-GM (1, N) | A new prediction algorithm by combining Verhulst and GM (1, N) models | | Nguyen et al. [18] | Fourier-NGBM (1, 1) | The Fourier transformation is used to correct the residuals of the NGBM (1, 1) model | | Wang et al. [19] | Hybrid model | A new hybrid forecasting model based on the Super-SBM DEA and GM (1, 1) model | | Guefano et al. [20] | Hybrid model | A combination of GM (1, 1) and VAR (1) | | Zhou et al. [21] | Hybrid model | A combination of GM (1, 1) and ARIMA | | Saxena [2] | IOGM | Grey forecasting models based on internal optimization |
| | Optimization based on data enhancement methods | | Wu et al. [22] | FGM (1, 1) | The author extends the traditional first-order accumulation operation to fractional-order accumulation operation and establishes GM (1, 1) model with fractional accumulation operation on this basis | | Ma et al. [23] | CFGM (1, 1) | Similar to the FGM model, the difference is that the fractional accumulation operation is replaced by the conformable fractional accumulation operation | | Chen et al. [24] | FHGM (1, 1) | Hausdorff fractional GM (1, 1) model | | Javed and Cudjoe [25] | DGM (1, 1, α) | Discrete GM (1, 1) with conformable fractional accumulation operation | | Şahin [26] | ROFANGBM (1, 1) | A novel optimized fractional nonlinear grey Bernoulli model with rolling mechanism | | Liu et al. [27] | WFDPGM (1, 1, tα) | DiscretePTGM (1, 1, α) with weighted fractional accumulation |
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