A General Definition of an Attribute Reduct

A reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of a given information table. A general definition of an attribute reduct is presented. Specifically, we discuss the following issues: First, there are a variety of properties that can be observed in an information table. Second, the preservation of a certain property by an attribute set can be evaluated by different measures, defined as different fitness functions. Third, by considering the monotonicity property of a particular fitness function, the reduct construction method needs to be carefully examined. By adopting different heuristics or fitness functions for preserving a certain property, one is able to derive most of the existing definitions of a reduct. The analysis brings new insight into the problem of reduct construction, and provides guidelines for the design of new algorithms.