An optimal black-start decision-making scheme plays an important role in the rapid recovery of a power system after a blackout.In the black-start decision-making process，uncertainties are inevitable.Specifically，some factors and weights having impacts on the black-start decision-making are better described as uncertain interval quantities or values.So far，the black-start decision-making problem with uncertain quantities described as interval values has not been investigated throughly.Given this，a black-start decision-making method capable of handling interval values and weights of indices is developed.An interval black-start decision-making matrix is first normalized by the error propagation theory;then，a linear goal programming model is presented to seek the ideal vector of index weights in the black-start decision-making based on the normalized matrix.The evaluation results with interval numbers are ranked on the basis of the risk attitude factors defined by the decision-makers.Finally，a scenario associated with a local power system is served for demonstrating the essential feature of the proposed method.Simulation results demonstrate that the developed interval-value based black-start decision-making method could better describe the actual decision-making process.