The divide and conquer method is a typical granular computing method using multiple levels of abstraction and granulations. So far, although some achievements based on divided and conquer method in the rough set theory have been acquired, the systematic methods for knowledge reduction based on divide and conquer method are still absent. In this paper, the knowledge reduction approaches based on divide and conquer method, under equivalence relation and under tolerance relation, are presented, respectively. After that, a systematic approach, named as the abstract process for knowledge reduction based on divide and conquer method in rough set theory, is proposed. Based on the presented approach, two algorithms for knowledge reduction, including an algorithm for attribute reduction and an algorithm for attribute value reduction, are presented. Some experimental evaluations are done to test the methods on uci data sets and KDDCUP99 data sets. The experimental results illustrate that the proposed approaches are efficient to process large data sets with good recognition rate, compared with KNN, SVM, C4.5, Naive Bayes, and CART.
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