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Scheduling tasks in distributed computing infrastructures (DCIs) is challenging mainly because the scheduler is facing a number of more or less dependent parameters that characterize the hosts coming from a particular computing environment and the tasks. In this paper we introduce a multi-criteria scheduling method for DCIs, aiming a better matching between hosts, and tasks waiting in a priority queue at a pull-based scheduler. The novelty of the approach consists in employing the Promethee  decision aid for selecting tasks. In the aim of computing preference relationships (priorities) among tasks, this approach performs pairwise comparisons of values that characterize tasks. The method exhibits interesting advantages, such as allowing the user to choose the values for the computation of the priorities, like the expected completion time (ECT) and cost. The approach is also very flexible, allowing through a set of parameters the specification of particular scheduling policies. To validate this method we built an XtrebWeb-like simulator, which is capable of running on real traces. We experiment on internet desktop grid (IDG), cloud and best effort grid (BEG), with various workloads. The results show that the Promethee-based scheduling method obtains good performance especially on IDG when certain fractions of the tasks fail. We also prove that multi-criteria scheduling using Promethee performs better than single-criterion scheduling, improving both makespan and cost. Also, a simple definition of ECT is the most efficient in terms of makespan. In this work we also explain the challenges of using Promethee for scheduling in DCIs.