## 5 Experimenting and Results
### ANFIS Results  
The application of ANFIS for the fuzzy prediction of the consequences of oil spills on the ground is presented in Figure 6. The initial parameters for the ANFIS model were as follows: (1) Gaussian MF; (2) 5 linguistic terms; and (3) 30 learning epochs (also see [80]).  
In Layer 1, the fuzzification of the input data is performed and MFs are obtained based on Equation (20). The input data is partitioned into five terms: \"Very High\", \"High\", \"Moderate\", \"Low\", and \"Very Low\" (Table 4), and is transformed into Gaussian MFs represented by \(\mu^{Gauss}\) (Equation (20)).  
The MFs of ground thickness (Input 1) and the corresponding intervals of five linguistic terms (Table 4) are presented in Figure 6. The MFs of other input variables are not shown since their graphical representation looks similar to Figure 7, only the interval values differ. This is because we used the Gaussian MF for all inputs.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Input Data** & & & & **Intervals (Terms)** & & \\ \hline \multirow{2}{*}{**Name of the Variable**} & **Value Range, Measurement Units** & & & & & \\  & **Input No.** & **Very Low** & **Low** & **Moderate** & **High** & **Very High** \\ \hline Ground thickness & [3; 5], m & Input 1 & [3; 3.65) & (3; 3.9) & (3.4; 4.6) & (4.1; 5) & (4.3; 5) \\ Spilled oil volume & [100; 10,000], m\({}^{3}\) & Input 2 & [100; 3500) & (100; 6000) & (1700; 8300) & (4000; 10,000) & (6000; 10,000) \\ Surface spreading & [5; 30], m\({}^{-1}\) & Input 3 & [5; 14) & (5; 20) & (9; 26) & (16; 30) & (23; 30) \\  coefficient & [750; 850], kg/m\({}^{3}\) & Input 4 & [750; 785) & (750; 810) & (765; 835) & (790; 850) & (815; 850] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Linguistic terms of input data.  
Figure 6: The proposed ANFIS network structure for oil spill prediction.  
In Layer 2, a set of initial fuzzy rules is formed based on combinatorial variants and Equation (19). As a result, we have 625 fuzzy rules. Every node in this layer is fixed or non-adaptive. In Layer 3, the normalization of rule strengths is performed based on Equation (21). In Layer 3, each node is also fixed. Fuzzy rule examples are presented in Table 5.  
Using an ANFIS intelligence, we obtained the prediction surfaces, two of which are presented in Figure 8. Figure 8a illustrates how the penetration of the oil spill (the penetrated OP) depends on the ground thickness (input 1) and the spilled oil volume (input 2).  
Figure 8: The results of the prediction of oil penetration with ANFIS.  
Figure 7: The MFs of ground thickness.  
depth it penetrates into the ground. Eventually, when a huge (i.e., \"high\") volume of oil spills (-5000 m\({}^{3}\)), it will pass into the groundwater.  
The defuzzification and application of fuzzy rules are performed in Layer 4 (see Equation (18)), where every node is adapted based on those rules. The global model response is obtained in Layer 5 using Equation (22).  
The output of the oil spill prediction ranges into five categories as follows: \"Very High\" [\(9.2\times 10^{6};1.5\times 10^{5}\)), \"High\" (\(1.4\times 10^{5}\); -\(6.2\times 10^{6}\)), \"Moderate\" (\(-6.1\times 10^{6}\); -\(1.3\times 10^{7}\)), \"Low\" (\(-1.2\times 10^{7}\); -\(-2.1\times 10^{7}\)), and \"Very Low\" (\(-2.0\times 10^{7}\); -\(2.9\times 10^{7}\)).