The current work demonstrates a novel multi-criteria decision-making (MCDM) technique to optimize the process parameters during the wire electric discharge machining of Inconel 718. A hybrid GRA-TOPSIS algorithm using entropy weights is developed to optimize wire electric discharge machining processes parameters for maximizing the cutting speed and simultaneously minimizing the surface roughness and flatness error. Experiments were conducted according to Taguchi L18 orthogonal array considering pulse on time, pulse off time, servo voltage, wire feed rate, and wire electrode types as the input parameters. The weights of each responses were calculated by entropy weights method. The different alternatives were ranked using the hybrid technique, and an optimum parameter combination is found that maximizes the process outcome. The analysis of variance (ANOVA) was performed to study the relative significance of process parameters on the performance index. The results were finally validated by performing confirmation tests. The entropy weighted GRA-TOPSIS method was observed to improve the overall process performance compared to conventional TOPSIS. Microstructural analysis, morphological studies, and EDS analysis were conducted to study the surface integrity of the machined surface under optimal parameter settings. © 2021, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.