Knowledge reduction in a new information view

Knowledge reduction is a very important issue in the rough set theory. In inconsistent decision tables, knowledge reduction under the traditional information view is not equivalent to that under the algebra view, and reducts obtained under the information view may not be reducts under the algebra view. In this paper we propose these new definitions of conditional entropy and attribute significance to overcome this problem. Because attribute significance under the new definition is able to reflect the change of the condition attributes distribution with respect to the positive region in the process of reduction, it is a better heuristic information compared with existing attribute significance. We also propose a complete heuristic algorithm for knowledge reduction. Empirical evidence shows that this algorithm is both efficient and tends to obtain minimal or optimal reducts.