| A majority of studies on rough set have focused on reduct construction from the original attribute set of an information table. A reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property as that of the entire set of attributes.; A general definition of an attribute reduct and a general definition of an approximate attribute reduct are presented in this thesis. We discuss the following issues: First, there are a variety of properties that can be observed and preserved in an information table. Second, the preservation of a certain property by an attribute set can be evaluated by different measures that are defined as different fitness functions. Third, based on the monotonicity property of a particular fitness function, the reduct construction methods are carefully examined. By adopting different heuristics or fitness functions for preserving a certain property, we are able to derive most of the existing definitions of a reduct.; The contribution of this thesis is two-fold. First, we present a critical review of rough set-based data analysis using reducts. Second, we analyze the criteria for calculating an attribute reduction. We divide the criteria into two parts, one for a reduct and the other for an approximate reduct. We give a general definition for each of them. We extend the application of reduct computation to other fields, i.e., clustering, association rules, in addition to classification. Different heuristics or fitness functions for preserving a certain property are investigated and implemented to classify most of the existing algorithms. Preliminary experimental results show that the proposed framework is effective and efficient. This study systematically summarizes the previous work, brings new insights into how research will be done in the future, and provides the guidelines for the design of new reduct computation algorithms. |
