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However, conventional scheduling methodology encounters a number of challenges. During the tasks scheduling in cloud systems, how to make full use of resources and how to effectively select resources are also important factors. At the same time, communication delay also plays an important role in cloud scheduling, which not only leads to waiting between tasks but also results in much idle interval time between processing units. In this paper, a fuzzy clustering method is used to effectively preprocess the cloud resources. Combining the list scheduling with the task duplication scheduling scheme, a new directed acyclic graph based scheduling algorithm called earliest finish time duplication algorithm for heterogeneous cloud systems is presented. Earliest finish time duplication attempts to insert suitable immediate parent nodes of the current selected node in order to reduce its waiting time on the processor. The case study and experimental results illustrate that the algorithm proposed in this paper is better than the popular heterogeneous earliest finish time algorithms. 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