Deep The research study focuses on the concept of Fuzzy Logic and its applications in diverse sectors like Behavioural Science, Machining, Business Operations, Medicinal Science, Water Quality Management, Manufacturing, Anti-Braking systems, etc. Fuzzy Logic is regarded as the best option to deal with complex problems which arise due to uncertainty, incomplete information, and lack of preciseness. The major focus of this research is then divided into a case study on the application of Grey Fuzzy Optimization in the Manufacturing and Machining sectors, using the Fuzzy Logic Toolbox of MATLAB. The case study deals with a Job-Shop Scheduling Problem in a Flexible Manufacturing System (FMS). Scheduling of Jobs is a crucial task for meeting and exceeding the market demands. The decision of which part will be the next to be processed considers some criteria that influence the performance of a job shop system. The job shop system is taken from previous literature and the proposed approach is applied to get the optimal scheduling of products. Within the vast field of production and operation, its applicability was tested in scheduling conflicts in flexible manufacturing systems (FMS). All the output values were in the range of single-digit percentage error owing to different sets of rule formations but nonetheless, the proximity of the actual and calculated values reaffirmed the confidence that the verification was justified.