We analyze the performances Of Fuzzy Batch Arrival Queuing System. Here the arrival rate, service rate, batch size, service cost and holding costs are all fuzzy numbers. Our idea is to transform the fuzzy inter arrival rate, service rate, batch size, service cost and holding costs into crisp values by applying ranking function method. We find the moderate and optimistic utilities by using the normalized and non-normalized fuzzy numbers. This method is most reliable method, simple to apply and can be used for all types of queuing problems.