On rule acquisition in incomplete multi-scale decision tables

Granular computing and acquisition of IF-THEN rules are two basic issues in knowledge representation and data mining. A rough set approach to knowledge discovery in incomplete multi-scale decision tables from the perspective of granular computing is proposed in this paper. The concept of incomplete multi-scale information tables in the context of rough sets is first introduced. Information granules at different levels of scales in incomplete multi-scale information tables are then described. Lower and upper approximations with reference to different levels of scales in incomplete multi-scale information tables are also defined and their properties are examined. Optimal scale selection with various requirements in incomplete multi-scale decision tables are further discussed. Relationships among different notions of optimal scales in incomplete multi-scale decision tables are presented. Finally, knowledge acquisition in the sense of rule induction in consistent and inconsistent incomplete multi-scale decision tables are explored.