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Preventive maintenance (PM) has been considered on many scheduling problems, however, the problem of scheduling jobs and PM on fuzzy job shop are seldom investigated. This paper presents a random key genetic algorithm (RKGA) for the problem with resumable jobs and PM in the fixed time intervals. RKGA uses a novel random key representation, a new decoding strategy incorporating maintenance operation, and discrete crossover. RKGA is applied to some instances to minimize the maximum fuzzy completion time. Computational results show the optimization ability of RKGA on fuzzy scheduling with PM.