Generalized Probabilistic Rough Sets Characterized by Fuzzy Sets

Theories of fuzzy sets and rough sets are useful for dealing with uncertain and vague knowledge in information systems. They are generalizations of classical set theory for modelling vagueness and uncertainty. Some integrations of them are expected to develop a model of uncertainty stronger than either. In this paper, we would like to study fuzziness in generalized probabilistic rough set model, which can be consider as an extension of to portray probabilistic rough sets by fuzzy sets. we also show how the concept of variable precision lower and upper approximation of a generalized probabilistic rough set can be generalized from the vantage point of the cuts and strong cuts of a fuzzy set which is determined by the rough membership function. As a result, the characters of the (strong) cut of fuzzy set can be used conveniently to describe the feature of variable precision rough set.