Efficient Algorithm for Attribute Reduction of Incomplete Information Systems Based on Assignment Matrix

Abstract

Rough set theory is emerging as a powerful toll for reasoning about data, attribute reduction is one of the important topics in the research on the rough set theory. At present, there are few researchers investigate attribute reduction based on incomplete decision table. Since computing attribute reduction of the incomplete decision table is more difficult than that of complete decision table. Now, some researchers used the assignment matrix method to design an attribute reduction algorithm based on the incomplete decision table. The time complexity of this algorithm is O(|C|³|U|²). In this algorithm, the key computation was computing the assignment matrix of the subset of condition attribute set B ⊆ C(denote MB). In the old algorithm, the time complexity for computing assignment matrix MB is O(|B||U|²). However, to lower the time complexity, we first provide an efficient algorithm for computing MB. The time complexity of the new algorithm is O(|U|²). To further improve the efficiency of attribute reduction algorithm, we reduce the unnecessary and repetitive computation of the old algorithm. Then we use the above algorithm to design an efficient algorithm of attribute reduction based on assignment matrix. The time complexity of the new algorithm is O(|C|²|U|²). At last, we use an example to illustrate the efficiency of the new algorithm.