Knowledge reduction of dominance-based fuzzy rough set in fuzzy decision system

Dominance-based rough set approach is an useful extension of the classical rough set approach and it has been successfully applied into multi-criteria decision analysis problems. This paper present an explorative research focusing on knowledge reduction of fuzzy rough set model in fuzzy decision system. The investigated fuzzy rough set model is different from the classical fuzzy rough set model because it is based on the dominance principle of memberships of objects on the attributes. We introduce the concept of reducts of fuzzy lower and upper approximations. They are minimal subsets of attributes which preserve the fuzzy lower and upper approximate memberships for each object belongs to the universe. The judgment theorems and discernibility matrixes associated with these two reducts are also obtained. An numerical examples is employed to substantiate the conceptual arguments.