## 4 Results and Discussions  
### Antis  
The fuzzy toolbox (\(\textit{>}\textit{fuzzy}\)) in MATLAB is used for the data training of ANFIS. There are eight membership function (MF) types under the Generate FIS menu. These are _trinf_, _trapmf_, _gbellmf_, _gaussmf_, _gauss2 mf_, _pinf_, _dsigmf_, and _psigmf_. Also, the values of the input set numbers (MFs) can be changed in this menu. In this study, the determined MF values are3 3, 4 4, 5 5, and 6 6. Necessary training has been undertaken in ANFIS for all function types with different input set numbers (MFs); the results are shown in Figure 4. In all training, the fault tolerance was selected as 0, and the epoch number was selected as 5000.  
As a result of 32 different trials seen in Figure 4, the ANFIS method with _gaussmf_ membership function, which has 6 6 input set numbers, provided the best performance. The minimum error results obtained are training root mean squared error (RMSE) = 1881.10; testing RMSE = 2291.24; training R\({}^{2}\) = 0.9753; testing R\({}^{2}\) = 0.9619; training root square error (RSE) = 1213.37; testing RSE = 808.03; training mean absolute error (MAE) = 0.39; and testing MAE = 0.21. Here, increasing the numbers of the input set and the epoch values changes the results positively.  
While calculating the error values, the following formulas were used:  
Root mean squared error (RMSE) [28] (\(A_{j}\) = actual values; \(P_{j}\) = predicted values; \(n\) = size of the data set):  
\[RMSE=\sqrt{\frac{1}{n}\sum\limits_{t=1}^{n}{\left({{A_{j}}-{P_{j}}}\right)^{2}}} \tag{1}\]  
Regression error (R\({}^{2}\)) [29]: (\(TSS\) = total sum of squares; \(RSS\) = residuals sum of squares).  
\[R^{2}=\frac{TSS-RSS}{TSS} \tag{2}\]  
Root square error (RSE) [30]:  
\[RSE=\sqrt{\sum\limits_{t=1}^{n}{\frac{{{\left({{P_{j}}-{A_{j}}}\right)}^{2}}} {{A_{j}}}}} \tag{3}\]  
Figure 4: ANFIS error values with different input set numbers. A: training RMSE; B: testing RMSE; C: training R2; D: testing R2; E: training RSE; F: testing RSE; G: training MAE; H: testing MAE.  
Mean absolute error (MAE) [31]:  
\[MAE=\frac{\sum\limits_{t=1}^{n}\Big{|}\frac{(P_{t}-A_{j})}{A_{j}}\Big{|}}{n} \tag{4}\]  
As seen in Figure 5b, the network has five layers; also, Figure 5c shows the network structrure (_Gaussmf_ 66). In this study, while the process was carried out with ANFIS, studies were carried out with different input set numbers (3 3, 4 4, 5 5, and 6 6). These can be increased or decreased by the user. However, there is no guarantee that the results will be better when increased. The most successful of these was the network with 66 entry sets. Figure 5b shows the network structure used in this study. The number of fuzzy rules is 36, and the number of nodes is 101. It also has input set numbers of 6 and 6, and its membership function is _gaussmf_. During the training, 3 and 3 input set numbers had nine fuzzy rules and 35 node numbers. Additionally, 4 and 4 input set numbers had 16 fuzzy rules and 53 node numbers. Further, 5 and 5 input set numbers had 25 fuzzy rules and 75 node numbers. When the number of input sets increased, it caused an increase both in the fuzzy rules and in the number of nodes of the network. In Figures 2 and 5a, ANFIS test results and actual experimental results are shown. By increasing the number of input sets and the epoch value, the similarity rate of the graphics can be changed. The neural network toolbox in the MATLAB/Simulink program (>nntool) was used during the training of all network structures except GRNN and RBNN. In all trials, the epoch number was set as 5000, and the target error value was 0. The training process of network structures for GRNN and RBNN was carried out by writing code; the target error value for these networks was 100.  
Figure 5: _Cont._