Abstract:

Reduction is one of the key problems in rough set theory. The widely used approaches to reduction include discernibility matrix and heuristic algorithm. To obtain the lower, upper approximate and boundary region distribution reduction in decision systems, congruence relations are defined on the power set of the conditional attributes and then the corresponding dependence spaces are constructed, from which the new approaches to the lower, upper approximate and boundary region distribution reductions are obtained. The judgment theorems for finding those reductions are also presented. An example is employed to demonstrate the conceptual argument. It provides a  new theoretical basis and technique for deleting redundant attributes in decision systems.