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This paper proposes to apply the concept of lower and upper approximations of rough sets to a backpropagation neural network (BPNN) training for transient stability assessment (TSA). The BPNN-based TSA problem is treated as a 'rough classification' problem with an indiscernible boundary region between the stable and the unstable classes. With the rough-set concept, a novel semi-supervised learning algorithm is used to train a BPNN to match the indiscernible boundary region of the input space. Based on the BPNN output, a 'rough classification' framework is proposed to classify the system stability into three classes-stable class, unstable class and indeterminate class boundary region. The introduction of the indeterminate class provides a feasible way to avoid the misclassifications normally occurring in BPNN-based TSA approaches, and the reliability of the classification results can hence be greatly improved. Applications of the proposed approach to two power systems demonstrate its validity for transient stability classification.