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This research attempts to explore the utilization of Gas-Assisted Electrical Discharge Machining (GAEDM) of die steel. High pressure inert gas (argon) in conventional electric discharge machining with constraint state was utilized to assess the surface roughness (SR). Analysis of Variance (ANOVA) was used to find out the process parameters that notably affected the SR. In this study, a mathematical model has been investigated to know the SR by using Buckingham pie-theorem. The fit summary confirmed that the quadratic model is statistically appropriate and the lack of fit is insignificant. Root mean square error and absolute standard deviation, obtained through response surface method (RSM), were also used for developing the model and for predicting its abilities through ANN, ANFIS. The experiment and anticipated estimates of SR during the process, obtained by RSM, dimensional analysis, ANN and ANFIS, were found to be in accord with each other. However, the ANFIS technique proved to be more fitting to the response as compared to the ANN, dimensional analysis and the RSM.