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Imprecise input data imposes special challenges to grid scheduling. This paper introduces a novel scheduler based on fuzzy optimization called IP-FULL-FUZZY which considers uncertainties of both application demands and of resource availability. The effectiveness of the proposed scheduler is compared to that of three non-fuzzy schedulers, as well as to that of a fuzzy scheduler which considers only uncertainties of application demands. Results of simulations considering diverse scenarios, based on characteristics of real networks and grid applications, evince the advantages of the proposed scheduler.