An axiomatic characterization of probabilistic rough sets

Probabilistic approaches were successfully applied to the theory of rough sets in recent decades. As a result, various types of probabilistic rough set models have been proposed in constructive approaches. This paper focuses on axiomatic approaches of probabilistic rough sets. Some new properties of probabilistic rough set approximation operators are examined in detail. By investigating the dependence among these properties, the axiom sets characterizing two types of the probabilistic rough set approximation operators are given. Each set of axioms guarantees the existence of an equivalence relation reproducing the corresponding probabilistic rough set approximation operators.

► Axiomatic approaches are first used for probabilistic rough sets.
► Some new properties of probabilistic rough sets are found.
► The dependence of the properties of probabilistic rough sets are first discussed, and two axiom sets are obtained.