On Dominance Relations in Disjunctive Set-Valued Ordered Information Systems

Set-valued information systems are generalized models of single-valued information systems. Its semantic interpretation can be classified into two categories: disjunctive and conjunctive. We focus on the former in this paper. By introducing four types of dominance relations to the disjunctive set-valued information systems, we establish a dominance-based rough sets approach, which is mainly based on the substitution of the indiscernibility relation by the dominance relations. Furthermore, we develop a new approach to sorting for objects in disjunctive set-valued ordered information systems, which is based on the dominance class of an object induced by a dominance relation. Finally, we propose criterion reductions of disjunctive set-valued ordered information systems that eliminate only those information that are not essential from the ordering of objects. The approaches show how to simplify a disjunctive set-valued ordered information system. Throughout this paper, we establish in detail the interrelationships among the four types of dominance relations, which include corresponding dominance classes, rough sets approaches, sorting for objects and criterion reductions. These results give a kind of feasible approaches to intelligent decision making in disjunctive set-valued ordered information systems.