## 6 Discussion  
Predictions with fuzzy inference and ML methods are now widely used in various fields of application, including the prediction of the impact of oil spills on the ground environment [13]. Although oil spills in the geological environment are not as large as oil spills on water, the entire consequences of such oil spills on the ground and their scale are not immediately visible due to the slow and gradual penetration of oil into the ground and groundwater. When oil penetrates groundwater, it can lead to massive pollution. Therefore, it is vital to predict oil spill penetration into groundwater in order to assess and evaluate the possible magnitude of the oil spill and prevent catastrophic consequences. However, given the peculiarities and characteristics of the oil spill process on the ground (see [13]), there is only a small amount of data on real oil spills. Consequently, we require an approach to attaining more data to apply fuzzy inference and ML methods for the prediction of the consequences of oil spills. As the results of related works and analyses show, various approaches to solving the issue of small datasets can be found in the literature. They are as follows: generating surrogate data, unsupervised learning, interpolation, and collecting data from users. We have found that generating surrogate data for the prediction of the consequences of oil spills is the most suitable for this research. On this basis, a mathematical model describing oil spill penetration into the groundwater process was developed [24], and necessary surrogate data was generated from existing data collected from real world oil spill accidents. Furthermore, we proposed the ANFIS-based approach for the prediction of the consequences of oil spills using small \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **MSE** & \(\mathbf{R^{2}}\) & **NRMSE** \\ \hline Linear Regression & 0.43 & 0.45 & 14.2\% \\ Decision Trees & 0.33 & 0.32 & 15.8\% \\ SVR & 0.52 & 0.54 & 19.1\% \\ Ensembles & 0.30 & 0.14 & 17.7\% \\ GPR & 0.12 & 0.95 & 4.3\% \\ The proposed & & & \\ ANFIS-based & 0.01 & 0.99 & 1.0\% \\ approach & & & \\ \hline \hline \end{tabular} Note that we can achieve better prediction results and better training of algorithms if we receive more real-world data from oil spill sites.  
\end{table} 
Table 6: Performance evaluation of the proposed approach with classifiers. sets of data and compared its predictive performance with several ML algorithms using the same set of data. The performance and effectiveness of the proposed ANFIS-based approach were compared with the chosen ML algorithms (Linear Regression, Decision Trees, SVR, Ensembles, and GPR) using the statistical measures of \(R^{2}\), NRMSE, and MSE. These measures showed better predictive performance and effectiveness of the proposed ANFIS-based approach for the prediction of the consequences of oil spills using small sets of data and the GPR algorithm. This result can be explained by the generalisation capability of ANFIS [81] and its stronger ability to deal with inaccurate and fuzzy input data for prediction than models based on mathematical Equation [24]. We also achieved better prediction results for Linear Regression (NRMSE = 14.2%) than with Decision Trees (NRMSE = 15.8%) and Ensembles (NRMSE = 17.7%), but this difference was not significant. However, the better statistical measuring of the Linear Regression algorithm can be explained by the small dataset (with low noise); as such, Linear Regression outperforms Decision Trees and Ensembles. Moreover, as can be seen in Figure 8b, the oil spill penetration into the ground surface depends on the volume of spilled oil (Input 2) and the oil density (Input 4), i.e., at certain values of spilled oil volume and oil density, spilled oil will spread more on the surface, and not penetrate into the ground. Therefore, we observed a curved surface to oil spill penetration which satisfies real oil spill cases.