An important and necessary feature of the real time system is tasks must complete their execution within a specified deadline. So tasks of these systems to be scheduled in such a manner that average execution time should be minimized along with less number of deadline miss. Earliest Deadline first until zero laxity (EDZL) is one such algorithm where a task is considered for scheduling based on laxity and deadline. If priority is considered in one of the steps of scheduling still minimizes the execution time and deadline miss. Hence a work is proposed by enhancing an Earliest Deadline first until Zero Laxity (EDZL) algorithm with fuzzy technique. Fuzzy technique EDZL algorithm (FTEDZL) schedules the task sets based on the priority generated by fuzzy inference system.