An Efficient Algorithm for Pawlak Reduction Based on Simplified Discernibility Matrix

Abstract

Since the definition of attribute reduction based on classic discernibility matrix is different from the definition of attribute reduction based on positive region, simplified discernibility matrix and the corresponding definition of attribute reduction are proposed. At the same time, it is proved that the proposed definition of attribute reduction is identical to the definition of attribution reduction based on positive region. For computing simplified discernibility matrix, IND(C) should usually be calculated at first, so a new algorithm for computing IND(C) is designed, whose temporal complexity is cut down to O(|C||U|). Furthermore, an efficient attribute reduction algorithm is proposed, whose temporal complexity and spatial complexity are cut down to $\max(O(|C|^2|U'_{pos}||U'|, O(|U||C|))$ and max (O(|C||U′ _pos ||U′|, O(|U|)) respectively. At last, an example is used to illustrate the efficiency of the new algorithms.