New attribute reduction based on rough set

With more than twenty years development, rough set theory has been successfully applied in the fields of expert systems, machine learning, and knowledge discovery in databases. Attribute reduction is an important research issue in rough set theory. At present, there are many different attribute reduction definitions, for example, attribute reduction based on Pawlak, based on information entropy and based on Skowron's discernibility matrix, etc. In this paper, a new measurement with parameter is provided based on rough set. Then monotony of the new measurement with parameter is proved. So definition of attribute reduction based on the new measurement with parameter is got. At the some time, it is proved that attribute reduction based on Skowron's discernibility matrix and on information entropy are the special cases of the new proposed attribute reduction. Therefore the new attribute reduction in rough set is very meaningful.