Knowledge reduction in random information systems via Dempster-Shafer theory of evidence

Knowledge reduction is one of the main problems in the study of rough set theory. This paper deals with knowledge reduction in (random) information systems based on Dempster-Shafer theory of evidence. The concepts of belief and plausibility reducts in (random) information systems are first introduced. It is proved that both of belief reduct and plausibility reduct are equivalent to classical reduct in (random) information systems. The relative belief and plausibility reducts in consistent and inconsistent (random) decision systems are then proposed and compared to the relative reduct and relationships between the new reducts and some existing ones are examined.