Sleep disorders are one of the causes of many diseases. Although the sleep stage classification is important for analyzing the sleep disorders, achieving the high classification accuracy is challenging. This paper is to address this issue. Here, various combinations of various signals including the single-channel electroencephalograms (EEGs), the combination of the single-channel EEGs and the electrooculograms (EOGs) together, the combination of the single-channel EEGs and the electromyograms (EMGs) together as well as the combination of the single-channel EEGs, the EOGs and the EMGs together are available. First, the fast Fourier transform approach is employed to decompose the signals into various components. Second, these components are decomposed into various bandlimited intrinsic mode functions via the variational mode decomposition. Third, various features are extracted from these intrinsic mode functions. Finally, the bootstrap aggregating (bagging) classifier is employed for performing the sleep state classification. The overall accuracy and the sensitivity are used as the metrics. Also, three publicly available databases are used for evaluating the performances of our proposed method. It is found that the combination of the single-channel EEGs, the EOGs and the EMGs together for performing the classification yields the higher classification accuracy, the higher sleep stage sensitivity and the better generality compared to other combinations of the signals. Moreover, our proposed method also outperforms the existing methods. This demonstrates the effectiveness of our proposed method. Besides, our proposed method provides a theoretical basis for performing the clinical sleep research.