On definability of sets in dominance-based approximation space

This paper introduces the representation of dominance-based approximation space by binary neighborhood systems introduced by Lin. We use blocks indexed by pairs of decision values as elementary neighborhoods or granules for computing approximations of generalized multiple criteria decision tables. The concept of generalized decisions was introduced by Dembczynski et al. as a generalization of DRSA (dominance-based rough set approach) where criteria and decision attribute in a decision table may be assigned a range of values. We show that binary neighborhood systems provide a uniform representation of both singleton and generalized multi-criteria decision tables. The main task is to determine the family of binary relations to capture inconsistency caused by violating the dominance principle. In addition, some interesting relationships among lower, upper approximations and boundary sets are presented. The proposed approach is demonstrated by examples.