## 4 Results and Discussion  
The LGP model is provided based on free software called \"Discipulus\"; its setting parameters are listed in Table 3. In addition, to provide the BRT model, the \"bag\" method of the \"fitresemble\" function of the Machine Learning Toolbox of MATLAB 2019 was implemented. The setting parameters for the BRT model are tabulated in Table 3, which were optimized to avoid overfitting by using a trial-and-error procedure [67; 68]. The kernel variable in the LWLR model was adopted through a trial-and-error process, leading to a value of 0.4. To provide the KStar model, the global blend--as a crucial parameter of the model--was optimized using a grid search scheme, leading to a value of 30. Figure 5 demonstrates the road map of predicting the procedure of BI parameters using provided AI models. This paper examines the LGP approach to predict the brittleness index (BI) based on four input variables: \(\text{R}_{\text{n}}\), \(\text{V}_{\text{p}}\), \(\text{D}\), and \(\text{Is}_{\text{50}}\). Also, two lazy machine learning models (namely LWLR and KStar) and a tree decision-based model (BRT) were measured to evaluate the outcome of the LGP approach. Figure 6 depicts the regression tree constructed from the BRT model, in which the terminal nodes or leafs identify the response of prediction. Table 4 presents the modeling results obtained by all models in the training and testing phases. The quantitative results in the training phase indicate that the KStar model (R = 0.9984, RMSE = 0.0865, MAPE = 0.2564, and \(\text{I}_{\text{A}}\) = 0.9992) is superior to the BRT (R = 0.9459, RMSE = 0.5297, and MAPE = 3.1569), LWLR (R = 0.9252, RMSE = 0.5960, and MAPE = 3.4088), and LGP (R = 0.9248, RMSE = 0.5867, and MAPE = 3.6279) models. Testing  
Figure 5: The road map of predicting BI using machine learning approaches. results show that the LGP approach exhibits the best efficiency for BI prediction by having the highest correlation coefficient (R = 0.9529) and lowest metrics error (RMSE = 0.4838 and MAPE = 3.2155), followed by LWLR (R = 0.9490, RMSE = 0.6607, and MAPE = 4.1549), BRT (R = 0.9433, RMSE = 0.6875, and MAPE = 4.3884), and KStar (R = 0.9310, RMSE = 0.9733, and MAPE = 5.0573), respectively. A scatter plot of each model, as a powerful graphical tool, is depicted in Figure 7 for comparison between predicted and observed values of BI. Careful examination of the scatters indicates that the LGP approach--due to the closest distribution of predicted points to the 1:1 line--demonstrates better performance than the other AI methods for whole data. The LWLR and BRT models, with acceptable accuracy and similar predictive performance, are ranked as the second and third best models, respectively. KStar, despite the remarkable performance in the training phase (R = 0.9984), is identified as the weakest method due to the highest dispersion of testing predicted points. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Metrics** & **LGP** & **K-Star** & **BRT** & **LWLR** \\ \cline{3-6}  & & R & 0.9248 & 0.9984 & 0.9459 & 0.9252 \\  & RMSE & 0.5867 & 0.0865 & 0.5297 & 0.5960 \\  & MAPE\% & 3.6279 & 0.2564 & 3.1569 & 3.4088 \\  & SI & 0.0463 & 0.0068 & 0.0418 & 0.0470 \\  & I\({}_{\rm A}\) & 0.9560 & 0.9992 & 0.9628 & 0.9531 \\  & St.D & 1.3339 & 1.5195 & 1.2640 & 1.2828 \\ \hline  & & R & 0.9529 & 0.9310 & 0.9433 & 0.9490 \\  & RMSE & 0.4838 & 0.7933 & 0.6875 & 0.6607 \\  & MAPE\% & 3.2155 & 5.0573 & 4.3884 & 4.1549 \\  & SI & 0.0389 & 0.0638 & 0.0553 & 0.0532 \\  & I\({}_{\rm A}\) & 0.9744 & 0.9095 & 0.9324 & 0.9400 \\  & St.D & 1.5059 & 1.0861 & 1.1116 & 1.1686 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Quantitative evaluation of AI base approaches for predicting BI. Figure 6: Decision trees of BRT model for prediction of BI. In the next graphical validation stage, half violin plots for all datasets are featured to show the distribution of quantitative data across several predicted values levels compared to observed ones.