We investigate the optimal scale selection and the attribute reduction problems in Wu-Leung information systems with a multi-scale decision. Firstly, the concept of entropy-based optimal scale selection is defined in a consistent Wu-Leung information system with a multi-scale decision, which can be used to characterize the optimal scale selection in the same system. Secondly, the concept of an entropy-based optimal scale selection for a single object is introduced, and an attribute reduction method based on the optimal scale selection is further presented. Finally, entropy-based optimal scale selection and attribute reduction methods for inconsistent Wu-Leung information systems with a multi-scale decision are explored.