A Complete Attribute Reduction Algorithm in Rough Set Theory

Rough sets theory is an effective mathematical tool dealing with vagueness and uncertainty. It has been applied in a variety of fields such as data mining, pattern recognition or process control. It is very important to compute the attribute reduction in real applications of rough set theory. To compute the optimal attribute reduction is NP-hard. Many heuristic attribute reduction algorithms with polynomial-time complexity have been proposed. However, most of them are incomplete for the definition of attribute reduction given by Z. Pawlak. and few of them are able to fully use the expert experience. In this paper, a complete attribute reduction algorithm based on the principle of discernibility matrix is given, which can make full use of the expert experience by defining a partial ordering relation on the set of condition attributes. The completeness of the algorithm is proved. The algorithm includes a random operation leading to different reductions may be obtained by repeating executing. Thus the quasi-optimal reduction can be got. Key-Words: Rough sets theory; Attribute reduction; Complete algorithm; Discernibility matrix