Micro Abrasive Jet Machining (μAJM) of glass materials is being used widely in MEMS and biomedical industries. Precise control of input parameters is necessary to obtain quality holes in these materials. In the present study, parameter optimization of AJM is carried out with a hybrid multi-criteria optimization technique namely Gray based Fuzzy Logic. The control variables used in this study include Nozzle diameter, Stand-off distance, Jet pressure and Angle of impact. The process performance measures taken in the studyinclude Material Removal Rate (MRR) and Radial Over Cut (ROC). The best parameter combination for maximum MRR was found at SOD 2.5 mm, angle of impact 85°, pressure 4.5 kgf/cm² and nozzle diameter 3.5 mm. The best parameter combination for minimum ROC was found at SOD 2.5 mm, angle of impact 85°, pressure 5 kgf/cm² and nozzle diameter 2.5 mm. Gray based Fuzzy Logic is conducted to determine the most influencing parameter for AJM with maximum MRR and minimum ROC. The angle of impact is found to be themost influencing parameter.