Efficient Attribute Reduction Algorithm Based on Incomplete Decision Table

Abstract

Rough set theory is emerging as a powerful toll for reasoning about data. Attribute reduction is one of important topics in the research on the rough set theory. At present, there is few researchers investigated 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, the designed attribute reduction algorithms based on incomplete decision table are no better than those based on complete decision table. The time complexity of the existed algorithm of attribute reduction based on incomplete decision table is O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> |U| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). To lower the time complexity, we first analyzed the shortcoming of those algorithms. And we provided an efficient algorithm for computing the tolerance class. Then we use the above algorithm to design an efficient algorithm of attribute reduction based on information quantity. The time complexity of the new is O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> |U| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ).