On generalization reducts in multi-scale decision tables

Abstract Real-world data is often organized at different levels of granularity with specified concept hierarchies. Multi-scale information tables represent such a type of data set in a hierarchical form. In this paper, we aim to focus on rule exraction in multi-scale decision tables. Unlike the case of attribute reduct, we consider a type of generalization reduct in multi-scale decision tables. This approach requires both the least number of attributes and the coarsest level of scales according to different reduct standards. The present study is conducted at the three different levels, that is, generalization reducts for objects, decision rules and multi-scale decision tables, respectively. The construction of granularity trees and the selection of cuts play a crucial role. At each level, we present various types of generalization reducts according to different requirements. The relationship between them is also investigated. Moreover, a comparative study between generalization reducts and attribute reducts is also performed. Based on the notion of generalization reducts, the procedure to extract the set of optimal decision rule in multi-scale decision tables is provided and an illustrative example is also given to show the proposed approach.