## 5 Conclusions  
Based on the conducted research regarding the modeling and optimization of circular cut quality performances in the plasma jet processing of aluminum alloy 5083, the next findings can be derived:  
* Experimental investigations according to the Taguchi L27 orthogonal array served as a solid foundation for examining the impact of the cutting speed, arc current, and cutting height on the circular cut quality responses: the circular kerf width, circular level angle, circularity error--top, and circularity error--bottom. * Artificial intelligence fuzzy logic technique combined with ANOVA proved as a good tool to define functional relations between process parameters and analyzed responses, as well as to discuss the effects of the parameters and their interactions with response variations. This confirmed high values of validation metrics such as the coefficient of determination and the mean absolute percentage error between the experimental and predicted response values. In this case, one of the confirmed benefits of the fuzzy logic technique is its ability to model complex manufacturing processes, such as plasma jet cutting, where imprecise and vague data sets are possible. * The novel hybrid grey-fuzzy approach for solving multiple circular quality response optimization problems was presented. By using it, optimal process parameter settings that result in minimal response objective functions were determined: v = 2000 mm/min, I = 65 A, H = 1.5 mm. * By analyzing 3D surface plots that show the influence of two process parameter variations on the GFRG values, a Pareto front of optimal solutions can be derived. This front corresponds to compromise solutions for the simultaneous optimization of circular quality responses. This front covers the next processing area: v = 2000 mm/min, I = 65 A, H = 1-1.5 mm/v = 2000 mm/min, I = 85 A, H = 2 mm. * ANOVA presented that the cutting speed has the largest influence on the GFRG, followed by the cutting height and arc current. * The validation experimental test confirmed the prediction and generalization capability of the developed circular quality responses as well as the GFRG fuzzy logic models. This was verified by calculating the mean absolute percentage errors between the newly received experimental and model-predicted data. * The optimal solutions presented in this paper, along with the novel hybrid grey-fuzzy approach, hold significant industrial relevance. Their practical application can enhance the process control and management, while also reducing manufacturing costs by minimizing post-processing procedures. \begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline \multirow{2}{*}{**Process Parameters**} & \multicolumn{2}{c}{**Circular Quality**} & \multirow{2}{*}{**Experimental**} & \multirow{2}{*}{**Predicted**} & \multirow{2}{*}{**MAPE (\%)**} & \multirow{2}{*}{**GRG**} & \multirow{2}{*}{**GFRG**} & \multirow{2}{*}{**MAPE (\%)**} \\  & & & & & & & \\ \hline \(v\) = 2000 mm/min & _Ckw_ (mm) & 1.91 & 1.79 & 5.76 & & & \\ \(I\) = 65 A & _\(\beta\)_ (\({}^{\circ}\)) & 1.29 & 1.17 & 8.58 & & & \\ \(I\) = 65 A & _Ce top_ (mm) & 0.059 & 0.061 & 4.40 & 0.756 & 0.722 & 4.46 \\ \(H\) = 1 mm & _Ce bottom_ (mm) & 0.095 & 0.102 & 7.68 & & & \\ \hline \(v\) = 2000 mm/min & _Ckw_ (mm) & 1.87 & 1.79 & 3.75 & & & \\ \(I\) = 65 A & _\(\beta\)_ (\({}^{\circ}\)) & 1.21 & 1.18 & 2.39 & 0.787 & 0.803 & 2.05 \\ \(H\) = 1.5 mm & _Ce top_ (mm) & 0.065 & 0.061 & 5.23 & & & \\ \hline \(v\) = 2000 mm/min & _Ckw_ (mm) & 2.15 & 2.12 & 1.01 & & & \\ \(I\) = 85 A & _\(\beta\)_ (\({}^{\circ}\)) & 1.15 & 1.09 & 4.69 & & & \\ \(H\) = 2 mm & _Ce top_ (mm) & 0.067 & 0.061 & 8.05 & 0.759 & 0.722 & 4.84 \\ \(H\) = 2 mm & _Ce bottom_ (mm) & 0.061 & 0.055 & 9.67 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Validation test of circular quality responses and GFRG fuzzy logic models. Future research in this area will focus on expanding the experimental domain and incorporating additional response variables into the analysis.