## 1 Introduction
When the ANN model was generated, its prediction accuracy was tested on data sets for validation and testing. A coefficient of correlation and mean squared error were applied as prediction accuracy measures when a comparison between the experimental and predicted response data was performed. Finally, the developed ANN model served for the creation of 3D response surface plots that visualize the process parameter effects on the analyzed response as well as to determine the optimal manufacturing process conditions that result in a minimal level angle. [PERSON] et al. [20] investigated the influence of the arc current, gas pressure, cutting speed, torch height, tool type, etc., on the dimensional accuracy, bevel angle, and dorsal height of circular cuts in the processing of a stainless steel sheet. The authors implemented the design of the experiments and the response surface methodology approach to discuss the process parameter effects, as well as to define regression mathematical models. Additionally, multi-response optimization was performed by a desirability analysis and a set of Pareto optimal solutions, that result in close-to-perfect cut quality characteristics, was derived. [PERSON] et al. [21] applied the Taguchi method combined with the Six Sigma approach to optimize the roundness of holes for the indicator light of large electrical switchboards. Hole-cut quality responses were defined by the bevel magnitude and diameter deviation. Factors that were analyzed in this paper are the air pressure, pierce time, tip size, feed rate, voltage, and ampereage. Authors generated S/N (signal-noise) ratio response graphs to define the optimal process parameter settings. Additionally, a test was applied to examine the effects of noise factors on response variables. Finally, after the overall optimal setting combination for the plasma jet manufacturing process was identified, confirmation runs were conducted and proved derived solutions. [PERSON] et al. (2012) performed the Taguchi optimization of the circular cuts level angle in the plasma jet cutting process of a mild steel plate. They took into consideration seven parameters: the plate thickness, cutting speed, arc ampere, arc voltage, air pressure, pierce height, and torch standoff distance. Authors calculated a S/N ratio for each experimental trial and derived diagrams according to the analysis of means (ANOM) technique. Using these diagrams, the optimum combination of parameter levels was identified. Additionally, interaction effects of the process parameters were discussed according to the generated interaction charts. Finally, ANOVA was conducted to discuss the percentage contribution of each process parameter effect on the analyzed level angle cut quality response. Based on the above literature review, it is visible that there is a space regarding the investigation of the plasma jet cutting process parameter effects on the circular cut quality responses when machining an aluminum alloy. As it is previously mentioned, processing aluminum by thermal manufacturing processes such as plasma can be very demanding and thus it represents a research challenge to determine the process parameter levels that enable close-to-optimum cut quality characteristics. Accordingly, this paper brings a valuable scientific contribution and investigates the influence of the cutting speed, arc current, and cutting height on circular quality responses such as the circular kerf width, circular bevel angle, and circularity error when cutting aluminum alloy 5083. Additionally, this paper presents a novel scientific methodology in solving the multi-response optimization problem, which means a hybrid approach that is a combination of grey relational analysis and the fuzzy logic technique. The grey-fuzzy hybrid approach enhances traditional GRA by integrating fuzzy logic, an artificial intelligence (AI) technique, to more effectively manage uncertainty and imprecise data--particularly prevalent in manufacturing processes.