## 3 Modeling of Circular Quality Responses
Such predicted responses data were marked by a yellow line in Figure 7a-d.  
Figure 4: Architecture of fuzzy logic system for modeling relations between plasma cutting process parameters and circular quality responses. Figure 5: Gaussian membership functions for inputs: (**a**) cutting speed, (**b**) arc current, and (**c**) cutting height. To evaluate the prediction accuracy of the developed fuzzy logic model for circular cut quality responses in the plasma jet cutting process of aluminum alloy 5083, a comparison was conducted between the experimentally obtained data and the model's predicted values. For each response comparison data set, the mean absolute percentage error (MAPE) and coefficient of determination (R\({}^{2}\)) were calculated as prediction validation measures. The comparison results are presented in Figure 7a-d. As it is obvious from Figure 7, the calculated mean absolute percentage errors and coefficients of determination as well as a comparison between blue and yellow lines prove good matching between the experimental and predicted responses data. The obtained results are valid strictly within the boundaries of the defined experimental design and are based on the specific combinations \begin{table}
\begin{tabular}{c p{341.4 pt}} \hline 1. rule: & If (cutting speed is L) and (arc current is L) and (cutting height is L) then (Ckw is MH) (\(\beta\) is MH) (Ce top is L) (Ce bottom is MH) \\ 2. rule: & If (cutting speed is L) and (arc current is L) and (cutting height is M) then (Ckw is ML) (\(\beta\) is M) (Ce top is M) (Ce bottom is VL) \\ 3. rule: & If (cutting speed is L) and (arc current is L) and (cutting height is H) then (Ckw is M) (\(\beta\) is M)(Ce top is ML) \\ 4. rule: & If (cutting speed is L) and (arc current is M) and (cutting height is L) then (Ckw is M) (\(\beta\) is VL) (Ce top is L) (Ce bottom is L) \\ 5. rule: & If (cutting speed is L) and (arc current is M) and (cutting height is M) then (Ckw is M) (\(\beta\) is VL) (Ce top is L) (Ce bottom is VL) \\ 6. rule: & If (cutting speed is L) and (arc current is M) and (cutting height is H) then (Ckw is H) (\(\beta\) is VL) (Ce top is M) (Ce bottom is MH) \\ 7. rule: & If (cutting speed is L) and (arc current is H) and (cutting height is L) then (Ckw is H) (\(\beta\) is VL) (Ce top is M) (Ce bottom is MH) \\ 8. rule: & If (cutting speed is L) and (arc current is H) and (cutting height is M) then (Ckw is H) (\(\beta\) is VL) (Ce top is M) (Ce bottom is ML) \\ 9. rule: & If (cutting speed is L) and (arc current is H) and (cutting height is H) then (Ckw is H) (\(\beta\) is VL) (Ce top is L) (Ce bottom is VL) \\ 10. rule: & If (cutting speed is M) and (arc current is L) and (cutting height is L) then (Ckw is L) (\(\beta\) is H) (Ce top is M) (Ce bottom is ML) \\ 11. rule: & If (cutting speed is M) and (arc current is L) and (cutting height is M) then (Ckw is L) (\(\beta\) is MH) (Ce top is MH) (Ce bottom is H) \\ 12. rule: & If (cutting speed is M) and (arc current is L) and (cutting height is H) then (Ckw is ML) (\(\beta\) is LH) (Ce top is H) (Ce bottom is H) \\ 13. rule: & If (cutting speed is M) and (arc current is M) and (cutting height is L) then (Ckw is ML) (\(\beta\) is HL) (Ce top is M) (Ce bottom is H) \\ 14. rule: & If (cutting speed is M) and (arc current is M) and (cutting height is M) then (Ckw is ML) (\(\beta\) is M) (Ce top is H) (Ce bottom is MH) \\ 14. rule: & If (cutting speed is M) and (arc current is M) and (cutting height is M) then (Ckw is ML) (\(\beta\) is M) (Ce top is M) (Ce bottom is MH) \\ \hline \end{tabular}
\end{table} 
Table 4: Fuzzy IF-THEN rules for modeling circular quality responses independent of process parameters: cutting speed, arc current, and cutting height. of parameters varied according to the experimental plan. Consequently, the predictive performance and reliability of the model apply primarily to this constrained design space.