Granular ball-based feature subset selection for incomplete generalized double multi-scale decision tables

One type of multi-scale data is widely available, where each object has values organized hierarchically across the same scale levels for all attributes and decisions. However, obtaining complete information can be challenging, leading to missing or omitted feature values. To address this issue, we propose a novel granular ball-based feature subset selection method in this paper. Firstly, we introduce a new multi-scale granular ball neighborhood decision table with multi-scale decisions, referred to as incomplete generalized double multi-scale decision tables (IGDMDTs). Secondly, we present an innovative approach to granulating objects into multi-scale granular ball neighborhood granules using the improved granular ball generation strategy. Next, we design a feature subset selection algorithm that optimizes both scale selection and feature selection. Additionally, we provide a concise rule acquisition algorithm. Finally, we verify the feasibility and effectiveness of our algorithm through experimental results.