Algorithm of Attribute Reduction in Dominance Based Rough Sets Combined with Dominance Discernibility Matrix

Dominance based rough set approach is a useful extension of the classical rough set approach and it has been successfully applied into multi-criteria decision analysis problems. This paper proposes the concept of dominance discernibility matrix and a novel attribute reduction algorithm based on dominance discernibility matrix. First, we employ dominance relation to detect the objects in the decision table, and get the dominance and subordinance classes according to condition attributes. Next, similarly, we apply dominance relation again to the decision table, and get upward and downward unions of decision classes according to decision attribute. Then we use dominance consistence method to calculate the objects in the decision table to generate the lower and upper approximations and discernibility matrix. Finally, we utilize discernibility matrix and its corresponding attribute reduction method to generate core of the decision table. A numerical example is employed to substantiate the conceptual arguments.