During the past decades, a great body of research has been devoted to automatic sleep stage scoring using the electroencephalogram (EEG). However, the results are not yet satisfactory to be used as a standard procedure in clinical studies. In this study, using recent developments in robust EEG phase extraction, a novel set of EEG-based features containing the Shannon entropy of the instantaneous analytical form envelope and frequencies of the EEG are proposed for sleep stage scoring. The proposed feature set is used to construct a distributed decision-tree classifier, with binary K-nearest neighbor classifiers at each decision node. The decision-tree structure is designed by brute-force-search over various combinations of the proposed feature set. The performance of the proposed approach is evaluated over two available sleep EEG data sets acquired using single-channel EEG. The first set contains 20 healthy young subjects containing equal number of male and female, and the second one has been acquired from 140 adult subjects from both genders, with sleep disorder. The performance of the proposed method is tested versus state-of-the-art classifiers. The results demonstrate that the proposed method, resulted in overall accuracies of 88.97% and 83.17% over the two data sets, respectively. Considering the high performance and simplicity of the proposed scheme, the method can be of interest for clinical sleep disorder studies.