A Method of Uncertainty Measure in Set-Valued Ordered Information Systems

Through the development of set-valued information systems from models of single-valued information systems, we see there are important applications in the pattern recognition and intelligent decision-making. In this paper, we first introduce concept of dominance rough entropy in set-valued ordered information systems. When the average uncertainty quantity of rough set is measured in set-valued ordered information systems, we not only consider the number of distinguishable pairs of the elements on the universe, but also increase factor of rough degree. Furthermore, the average uncertainty quantity of rough set with respect to the dominance relation is defined. Finally, by use of a case, we prove that average uncertainty quantity of rough sets with respect to the dominance relation in a set-valued ordered information system drops monotonously with decrease of knowledge granularity. These results come up with a feasible method to acquire knowledge in set-valued ordered information systems.