Interpretation of Belief Functions in The Theory of Rough Sets

This paper reviews and examines interpretations of belief functions in the theory of rough sets with finite universe. The concept of standard rough set algebras is generalized in two directions. One is based on the use of non-equivalence relations. The other is based on relations over two universes, which leads to the notion of interval algebras. Pawlak rough set algebras may be used to interpret belief functions whose focal elements form a partition of the universe. Generalized rough set algebras using non-equivalence relations may be used to interpret belief functions which have less than |U | focal elements, where |U | is the cardinality of the universe U on which belief functions are defined. Interval algebras may be used to interpret any belief functions.