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We suggest a fuzzy based scheduling policy, which not only considers the distributed ownerships and heterogeneous environments but also handles the dynamic state of the cluster (load etc) more effectively. The algorithm aims at finding the best schedule for the combined set of jobs using fuzzy logic. Two fuzzy membership functions, resource fuzzy set and priority fuzzy set, are computed based on each job's requirements against each available node and user priority and are combined using a convex combination of fuzzy numbers to arrive at a final fuzzy value. This value indicates the extent to which the job can be executed on the given node. The result, of this formulates a score matrix, which is converted to a cost matrix and solved for minimum cost using the Hungarian approach of assignment. One of the important factors in this approach is that of deciding weights for the resources. We argue that the weights …