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The authors investigate a robust supervisory control problem based on the model of fuzzy discrete event systems. If there are uncertainties in the systems, the model can be assumed to belong to a model set. For all possible models in the set, necessary and sufficient conditions for the existence of a supervisor to achieve the given fuzzy language specification are obtained under complete and partial observations. The relation between the controllability (and observability) with respect to the models and their upper bound is given, based on which the equivalent conditions for the existence of a supervisor are obtained.