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Finding an optimal black-start scheme plays an important role in speeding up the restoration procedure of a power system after a blackout or a local outage. In a practical black-start decision-making procedure, uncertainties are inevitable. Some factors such as index values and indexes’ weights can be better described as uncertain interval values. So far, the black-start decision-making problem with uncertainties has not yet been systematically investigated. Given this background, a new approach for black-start decision-making based on interval values is developed. First, a decision-making matrix with interval values is normalized by using the error propagation theory. Then, a linear goal programming model is developed to seek the ideal vector of index weights and the evaluation values of all candidate black-start schemes can be obtained. A risk attitude factor based method is presented to sort the schemes. Finally, a sample example is served for demonstrating the essential feature of the proposed method, and comparisons with three existing methods are also carried out. Simulation and comparison results show that the proposed method could not only take different kinds of uncertainties into account, but also overcome several shortcomings of the existing methods. [ABSTRACT FROM AUTHOR]