## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Predictive** & \multicolumn{2}{c}{**Input**} & \multirow{2}{*}{**Stages**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**MAE**} & \multirow{2}{*}{**LMI**} & \multirow{2}{*}{**CC**} & \multirow{2}{*}{**WI**} & \multirow{2}{*}{**SRMSE**} \\
**Models** & **Combination** & & & & & & & & \\ \hline
**ANFIS-GA** & **Model-16** & **Train** & **0.286** & **0.224** & **0.632** & **0.924** & **0.959** & **16.358** \\
**ANFIS-GA** & **Model-16** & **Test** & **0.296** & **0.243** & **0.610** & **0.930** & **0.962** & **18.477** \\ ANFIS-GA & Model-17 & Train & 0.317 & 0.243 & 0.601 & 0.906 & 0.950 & 18.103 \\ ANFIS-GA & Model-17 & Test & 0.366 & 0.268 & 0.570 & 0.893 & 0.944 & 22.812 \\ ANFIS-GA & Model-18 & Train & 0.467 & 0.370 & 0.392 & 0.783 & 0.874 & 26.649 \\ ANFIS-GA & Model-18 & Test & 0.491 & 0.405 & 0.349 & 0.806 & 0.894 & 30.637 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._uncertainties are \(RMSE\) = 0.691, 0.403; \(MAE\) = 0.649, 0.424; \(LMI\) = 0.649, 0.424; \(CC\) = 0.687, 0.482; \(WI\) = 0.806, 0.702, and \(SRMSE\) = 0.806, 0.403, respectively. Based on the minimal absolute error metrics (i.e., RMSE, MAE, and SRMSE), the model uncertainty was higher as compared to variable and data uncertainty. To finalize the best relation between proposed models and the performance metrics, a heat map was created, where this diagram depicts the graphical comparison between models in term of standardized performance indices. It can be seen in Figure 3 that all the standardized performance indices of ANFIS-PSO (Model-7) have a dark blue color (best performance) in both training and testing phases, while ANFIS-ACO (Model-16) appeared to be the lowest in terms of these performance metrics (dark red color). The scatter plots were generated between observed and predicted \(Ss\) for the cases of training and testing phases to strengthen the visualization of the applied model's performance accuracy with the correlation coefficient (\(R\)) magnitude (Figure 4). The ANFIS-PSO model was revealed to have better correlation in comparison with the other applied models by achieving higher \(R\) value as follows: (ANFIS-PSO \(\approx\) 0.9611, ANFIS \(\approx\) 0.936, ANFIS-GA \(\approx\) 0.9237, ANFIS-DE \(\approx\) 0.865, ANFIS-ACO \(\approx\) 0.863) in training phase and (ANFIS-PSO \(\approx\) 0.9611, ANFIS \(\approx\) 0.936, ANFIS-GA \(\approx\) 0.9237, ANFIS-DE \(\approx\) 0.869, ANFIS-ACO \(\approx\) 0.869) in the testing phase. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **RMSE** & **MAE** & **LMI** & **CC** & **WI** & **SRMSE** \\ \hline Model Uncertainty & 0.691 & 0.649 & 0.649 & 0.687 & 0.806 & 0.691 \\ Variable Uncertainty & 0.403 & 0.424 & 0.424 & 0.482 & 0.702 & 0.403 \\ Data Uncertainty & 0.334 & 0.383 & 0.340 & 0.348 & 0.332 & 0.404 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The uncertainty analysis of the proposed model-based IQR of indices. Figure 3: Heat map of the applied hybrid predictive models: (**a**) Training stage and (**b**) Testing stage. Figure 4: Scatter plots presentation between the observed and predicted values of computed shear strength for the best input combination and models: (**a**) Training stage and (**b**) Testing stage. To establish the relationship of the interquartile range (IQR) between observed and predicted _Ss_ by various proposed models, the boxplots of both training (yellow) and testing (green) phases were displayed in Figure 5. The distinction of performances is visible since the prediction was generated via ANFIS-PSO (Model-7) against observed (experimental) _Ss_, which were significantly accurate in comparison with ANFIS (Model-8), ANFIS-GA (Model-16), ANFIS-DE (Model-13), and ANFIS-ACO (Model-16). Hence, the boxplots, together with the benchmark models against observed _Ss_, ascertain the better accuracy of ANFIS-PSO model. To scale the degree between predicted and experimental _Ss_ of HSC for all proposed hybrid and standalone ANFIS models, a Taylor diagram was drawn (Figure 6).