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In this study, the effect of machining parameters on Ra (average surface roughness), Rq (quadratic average roughness) and Rz (maximum roughness) values were measured on the material cut surface as a result of machining Inconel 718 (IN718) superalloy on a CNC wire erosion machine were investigated. As the processing parameters; voltage, wire feed rate and dielectric fluid pressure were determined. In the experiments, pure water was used as the dielectric fluid and 0.3 mm brass wire was used as the wire. The aim of the study is to determine the optimum values of the cutting parameters in order to obtain the lowest Ra, Rq and Rz values. Gray Relational Analysis (GRA), which is one of the multi-criteria decision-making methods, has been applied for the optimization of the machining parameters in the cutting process with the wire erosion machine. The experiments and the levels of the parameters used were designed and optimized according to the Taguchi L9 (33) orthogonal array. Analysis of Variance (ANOVA) was used to determine the effect percentages of the cut-off parameters. The parameter with the highest effect was determined as voltage with a ratio of 79.18% for Ra, 84.05% for Rq, and 89.25% for Rz. The lowest Ra, Rq and Rz values were obtained as 0.123 μm, 0.178 μm and 0.740 μm, respectively. [ABSTRACT FROM AUTHOR]