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Task scheduling is an important research direction in cloud computing. The current research on task scheduling considers mainly the design of scheduling strategies and algorithms and rarely gives attention to the influences of uncertain factors, such as the network bandwidth and millions of instructions per second (MIPS), on the scheduling process. The network bandwidth and MIPS directly affect the performance of a virtual machine (VM), which further influences the scheduling performance. In this paper, uncertain factors are transformed into interval parameters. The make-span, scheduling cost, load balance, and task completion rate are simultaneously considered in the scheduling process. Then, an interval many-objective cloud task scheduling optimization (I-MCTSO) model is designed to simulate real cloud computing task scheduling. To implement this model, an interval many-objective evolutionary algorithm (InMaOEA) is proposed. An interval credibility strategy is employed to improve the convergence performance. The hyper-volume and degree of overlap based on the interval congestion distance strategy are used to increase the population diversity. Simulation results demonstrate the effectiveness and superior performance of InMaOEA in comparision with other algorithms. The proposed approaches can provide decision-makers with an efficient allocation plan for cloud task scheduling. [ABSTRACT FROM AUTHOR]