A kind of unrelated parallel machines scheduling problem is discussed. The memberships of fuzzy due dates denote the grades of satisfaction with respect to completion times with jobs. Objectives of scheduling are to maximize the minimum grade of satisfaction while makespan is minimized in the meantime. Two kind of genetic algorithms are employed to search optimal solution set of the problem. Both Niched Pareto Genetic Algorithm (NPGA) and Nondominated Sorting Genetic Algorithm (NSGA-II) can find the Pareto optimal solutions. Numerical simulation illustrates that NSGA-II has better results than NPGA.