Rule acquisition in generalized multi-scale information systems with multi-scale decisions

In this paper, knowledge acquisition in the sense of deriving IF-THEN rules in multi-scale information systems with multi-scale decision attributes is investigated. Specifically, the concept of a generalized multi-scale information system with a multi-scale decision attribute, called generalized multi-scale decision information table (GMDIT for short), is first introduced. Such a system is a multi-scale decision table in which each condition or decision attribute at each object can take different values under different scales. The notion of scale selections for a GMDIT, which is mainly used to determine individual decision tables, is then defined. Information granules and their properties with different scale selections in GMDITs are also described. Optimal scale selections which are used to determine proper decision tables for final decision in inconsistent GMDITs are further formulated. Local optimal scale selections to obtain more concise decision rules for different objects are presented. Finally, attribute reducts based on optimal scale selections are derived and decision rules hidden in inconsistent GMDITs are unraveled.