Comparative Research of Attribute Reduction based on the New Information Entropy and on Skowron´s Discernibility Matrix

The attribute reduction definitions based on algebra view, based on information entropy view and based on Skowron´s discernibility matrix are familiar in rough set theory. It was proved that these three definitions of attribute reduction are not equivalent to each other. Recently, some researchers provided a new entropy method for decision table. And based on this method, a new information view that could comprehensively illustrate the algebra view is introduced. For getting the illustration of the attribute reduction based on Skowron´s discernibility matrix with information view, it is proved that the new attribute reduction definition based on the new information entropy proposed by other researchers is equivalent to that based on Skowron´s discernibility matrix. It will also provide more ways to design efficient algorithm of attribute reduction based on Skowron´s discernibility matrix.