Knowledge Reduction and Rule Extraction in Set-valued Decision Information System

In this paper we describe the incomplete information system by the set-valued information system. The two relations are defined in set-valued decision information system: the tolerance relation and the dominance relation. The rough approximation on these relations is defined, and the different properties of a set-valued information system based on these two relations are studied. Then we give the judgment theorems and the discernibility matrices of the generalized decision reduction in set-valued decision information system based on these relations, from which we provide a material approach to knowledge reduction. Finally, the optimal generalized decision rules are discussed based on these two relations.