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Manufacturing requires reliable models and methods for the prediction of output performance of machining processes as the demand for highly automated machine tools in the industry has been increased. The prediction of optimal machining conditions for good surface finish and dimensional accuracy plays a very important role in process planning. In the present work, dry turning of austenitic Stainless Steel (SS303) using CVD multi-layer (TiN/Al2O3/TiCN) coated carbide insert has been investigated. Cutting speed, feed rate, and depth of cut have been considered as the input process variables for the dry turning process. Taguchi's L9 orthogonal array has been utilized for designing the experiments. A Grey-Fuzzy logic approach has been employed to investigate the multi-objective optimization of turning process parametric combination to provide minimum Surface Roughness (SR) with the maximum Material Removal Rate (MRR). Analysis of Variance (ANOVA) technique has been employed to identify the most influencing input process variable for achieving minimum SR and maximum MRR. Morphology analysis has been performed on the machined surfaces and the chips generated during the machining processes using a Scanning Electron Microscope (SEM) in order to relate the surface quality with the input factor setting.