## 3 Results
### Comparison of ANFIS and ANN Performance Results  
To evaluate the performance of the ANFIS model, a performance comparison with the ANN model was carried out. Studies on the comparison of the performances of ANFIS and ANN models, model outputs, and errors were shown in [47; 49]. In the literature, studies have been conducted comparing the performances, model outputs, and errors of ANFIS and ANN models [47; 48; 49; 50]. The estimation results and performance metrics of ANN and ANFIS models are presented in Table 2.  
When the performance metrics of the ANFIS and ANN models were examined, it was observed that the ANFIS estimation results were more consistent compared to the ANN model. However, in the 2.50 Cross-Correlation test result in Table 2, it was determined that the ANN provided better results than the ANFIS. The comparison of FSANNCO and FSACO model results with the target FCS data, using the training data for the 3.25 mm electrode and 2.50 mm electrode, is shown in Figures 15 and 16. In Figures 15 and 16, although the tracking trends of FSACO and FSANNCO with the target FCS show similarities, it is observed that FSACO is more successful in capturing FCS changes. As shown in Figures 15 and 16, it has been observed \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Phase** & **R-Squared** & **Cross-Correlation** & **RMSE (A)** \\ \hline ANFIS 3.25 & Train & 0.7033 & 0.9587 & 32.6174 \\ \hline ANFIS 3.25 & Test & 0.6449 & 0.9565 & 33.5493 \\ \hline ANFIS 2.50 & Train & 0.7640 & 0.9598 & 29.4357 \\ \hline ANFIS 2.50 & Test & 0.5853 & 0.9323 & 38.9470 \\ \hline ANN 3.25 & Train & 0.6842 & 0.9559 & 33.6504 \\ \hline ANN 3.25 & Test & 0.6417 & 0.9554 & 33.7037 \\ \hline ANN 2.50 & Train & 0.7364 & 0.9550 & 31.1072 \\ \hline ANN 2.50 & Test & 0.5412 & 0.9349 & 40.9669 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Training and testing of results of ANFIS and ANN. Figure 14: Performance analysis of the ANN model with training data for the 2.50 mm electrode: (**a**) comparison of target FCS with FSANNCO; (**b**) cross-correlation between the target FCS and FSANNCO. that FSACO produces more stable results, particularly at low current levels and during sudden current changes. Additionally, it has been observed that FSACO is more effective in capturing dynamic changes in the welding arc during transitions between different current levels compared to FSANNCO. In Figure 17a,b, the test data results of the ANN model for 2.50 and 3.25 mm electrodes are shown and compared with FSANNCO and the target FCS. Figure 17a shows that although FSANNCO tracks the FCS effectively, it experiences deviations in the transition regions. In contrast, Figure 17b reveals a more stable performance of FSANNCO in tracking the FCS graph. When the performance metrics and graphical analyses of ANFIS and ANN models are examined, it is observed that ANFIS achieves higher R-squared values and lower RMSE values when compared to ANN. The primary reason for this performance difference lies in ANFIS's hybrid structure, which combines the advantages of fuzzy inference systems and  
Figure 16: Comparison of FSANNCO and FSACO with FCS with training data for 2.50 mm electrode. Figure 15: Comparison of FSANNCO and FSACO with FCS with training data for 3.25 mm electrode. neural networks [47; 49]. The superiority of ANFIS becomes particularly evident in areas such as modeling nonlinear data [29; 47] and effectively managing uncertainties. ANFIS offers a more flexible model than ANN due to its integration of fuzzy inference systems. As shown in Figures 15 and 16, it was observed that FSACO was more effective than FSANNCO in capturing the dynamic changes in the welding arc during transitions between different current levels. In contrast, ANN models are more sensitive to model parameters such as the number of layers, number of neurons, and learning rate. As a result, their performance may decline, particularly when dealing with complex and uncertain datasets.