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Multi-scale decision system (MDS) is an effective tool to describe hierarchical data in machine learning. Optimal scale combination (OSC) selection and attribute reduction are two key issues related to knowledge discovery in MDSs. However, searching for all OSCs may result in a combinatorial explosion, and the existing approaches typically incur excessive time consumption. In this study, searching for all OSCs is considered as an optimization problem with the scale space as the search space. Accordingly, a sequential three-way decision model of the scale space is established to reduce the search space by integrating three-way decision with the Hasse diagram. First, a novel scale combination is proposed to perform scale selection and attribute reduction simultaneously, and then an extended stepwise optimal scale selection (ESOSS) method is introduced to quickly search for a single local OSC on a subset of …