Probabilistic approaches to rough sets

Probabilistic approaches to rough sets in granulation, approximation and rule induction are reviewed. The Shannon entropy function is used to quantitatively characterize partitions Of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approximations are defined in a decision-theoretic framework. The problem of rule induction, a major application of rough set theory, is studied in probabilistic and information-theoretic terms. Two types of rules are analyzed the local, low order rules, and the global, high order rules.