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Grid scheduling is essential to Quality of Service provisioning as well as to efficient management of grid resources. Grid scheduling usually considers the state of the grid resources as well application demands. However, such demands are generally unknown for highly demanding applications, since these often generate data which will be transferred during their execution. Without appropriate assessment of these demands, scheduling decisions can lead to poor performance. Thus, it is of paramount importance to consider uncertainties in the formulation of a grid scheduling problem. This paper introduces the IPDT-FUZZY scheduler, a scheduler which considers the demands of grid applications with such uncertainties. The scheduler uses fuzzy optimization, and both computational and communication demands are expressed as fuzzy numbers. Its performance was evaluated, and it was shown to be attractive when communication requirements are uncertain. Its efficacy is compared, via simulation, to that of a deterministic counterpart scheduler and the results reinforce its adequacy for dealing with the lack of accuracy in the estimation of communication demands.