The SKD-11 steel was machined by the hybrid surface-electro discharge diamond grinding (S-EDDG) machining process with an aim to determine the optimum setting of process parameters for multi-output optimization and thereafter developed the mathematical-models of material-removal-rate (MRR), and surface-roughness (Ra) through the Dimensional Analysis method. In this research work, Grey-Taguchi based Fuzzy method is utilized for multi-output optimization of process parameters. The various process-variables selected in this research work are current, voltage, wheel speed, pulse-on-time, duty-cycle, and nozzle flushing aid. Total 18 experiments have been conducted on S-EDDG set-up according to Taguchi’s L18 orthogonal array. The response table and Analysis of Variance investigation are used to determine the optimum setting of process control-parameters and further help to determine the impact of these control-factors on the multi-output performance index (MPI). In this research work, the Dimensional Analysis method is utilized for the development of mathematical models of MRR, and Ra. The experimental results and predicted estimation of values from the developed models were compared and showed satisfactory matching between them. The optimum combination of process variables suggested by the hybrid optimization method was validated through confirmation experiment whose result depicts that aimed MPI is significantly improved by 0.435. The suggested optimum setting of process variables helps the production engineer to set-up the economical-cum-efficient process.