Representation of second-order Dominance-based approximation space by neighborhood systems

This paper introduces the representation of generalized dominance-based decision tables by neighborhood systems. Dominance-based rough set approach (DRSA) introduced by Greco et al. is a useful tool for multi-criteria data analysis problems. Recently, Dembczynski et al. introduced the concept of generalized decisions as a generalization of the DRSA where criteria in a decision table may be assigned a range of values. We use blocks indexed by pairs of decision values as elementary neighborhood systems for computing approximations of generalized decision tables. Each generalized decision table is represented by a pair of lower and upper singleton decision tables, which are represented by a pair of elementary neighborhood systems. A generalized decision table is definable if both its lower and upper singleton decision tables are definable. In addition, we introduce two simple algorithms based on minimum and maximum operations for making a decision table definable. The proposed approach is demonstrated by examples.