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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 864652, 24 pages
http://dx.doi.org/10.1155/2012/864652
Research Article

Knowledge Reduction Based on Divide and Conquer Method in Rough Set Theory

Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 27 June 2012; Revised 18 September 2012; Accepted 2 October 2012

Academic Editor: P. Liatsis

Copyright © 2012 Feng Hu and Guoyin Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.