Theory And Approach Of Knowledge Reduction In Set-valued Information System

Set-valued information systems are generalized models of single-valued information systems.Knowledge reduction is one of the hot research topics of rough set theory. Therefore, we proposeattribute reductions of set-valued information systems, which is an important research directionin generalized models of Pawlak rough set.This paper is based on rough sets,in the partial order of binary relation,we present knowl-edge reduction approach￠lower approximation IR. Furthermore, judgement theorem and dis-cernibility matrix are obtained. In set-valued information systems, object set divided by thebest set,we give approaches to extracting decision rules .There are strong connections between rough set theory and Dempster-Shafer theory ofevidence. It has been demonstrated that various belief structures are associated with variousrough approximation spaces, such that the diferent dual pairs of upper and lower approximationoperators induced by rough approximation spaces may be used to interpret the correspondingdual pairs of plausibility and belief functions . In this paper, we introduce the evidence theoryin set-valued information systems, and discuss the specific approaches to attribute reductions inset-valued information systems based on evidence theory.Information granularity and entropy theory are two important measure ways of the un-certainty study of the information system .In this paper,we introduce concepts of informationgranularity and entropy in set-valued information systems, give some basic properties of infor-mation granularity and entropy,and make an explaination with specific examples.