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Preemptive scheduling problem of a single machine subject to arbitrary release dates under uncertain situation is discussed. The release dates of jobs are independence and different with each other. Uncertainty means due dates are not accurate, which can be described by fuzzy set. The memberships of fuzzy due dates denote grade of satisfaction of completion times of corresponding jobs. The objective of the problem is to find an optimal schedule which maximizes the minimal grade of satisfaction of jobs completion times with respect to fuzzy due dates. By extending the method of corresponding problem with accurate due dates into fuzzy situation for the problem, an O(n2) algorithm is presented.