Dominance-based rough sets using indexed blocks as granules

Abstract

Dominance-based rough set introduced by Greco et al. is an extension of Pawlak's classical rough set theory by using dominance relations in place of equivalence relations for approximating sets of preference ordered decision classes satisfying upward and downward union properties. This paper introduces a formulation of approximation spaces based on multiple criteria decision tables by using the concept of indexed blocks, which are sets of objects indexed by pairs of decision values. The approximations of sets of decision classes are formulated in terms of exclusive neighborhoods of indexed blocks. We show that the set of indexed blocks with exclusive neighborhoods forms a partition on the universe of objects when approximating preference ordered decision classes with upward and downward union properties. Examples are given to illustrate presented concepts.