Approximate Dominance-Based Rough Sets Using Equivalence Granules

The rough set theory introduced by Pawlak has provided a solid foundation for developing many useful learning algorithms and tools for data analysis. Dominance-based rough set introduced by Greco et al. is an extension of classical rough sets for dealing with multiple criteria decision analysis problems. In this paper, we look into the relationship between the two theories and introduce a procedure for approximating dominance-based rough sets by a family of equivalence relations. We use the concept of indexed blocks to represent dominance-based approximation space, and it is assumed that the family of indexed blocks Forms a partition on the universe of objects. Objects in lower approximations are used to approximate the dominance-based approximation space. An example is given to illustrate the feasibility of our approach.