Generalized attribute reduct in rough set theory

Attribute reduction plays an important role in the areas of rough sets and granular computing. Many kinds of attribute reducts have been defined in previous studies. However, most of them concentrate on data only, which result in the difficulties of choosing appropriate attribute reducts for specific applications. It would be ideal if we could combine properties of data and user preference in the definition of attribute reduct. In this paper, based on reviewing existing definitions of attribute reducts, we propose a generalized attribute reduct which not only considers the data but also user preference. The generalized attribute reduct is the minimal subset which satisfies a specific condition defined by users. The condition is represented by a group of measures and a group of thresholds, which are relevant to user requirements or real applications. For the same data, different users can define different reducts and obtain their interested results according to their applications. Most current attribute reducts can be derived from the generalized reduct. Several reduction approaches are also summarized to help users to design their appropriate reducts.