Reduction of rough approximation space based on matroid

In this paper, we firstly review the definitions and matrix representations of a special pair of upper and lower approximation operators generated by a reflexive and transitive binary relation. Then the matroid generated by the reflexive and transitive binary relation of rough approximation space and its properties are discussed. Simultaneously, we consider how to generate a rough approximation space by a matroid (satisfying ∀X ⊆ U, ∀y ϵ X, if x ∉ d(y) or y ∉ d(x), then |d(X∪{x})| = |d(X)|+|d(x)|), and we get that the special upper approximation operator equals to the closure operator in the matroid. Moreover, we give the axiomatization characterization of the rough approximation operators. Finally, we give an algorithm to reduce the information system using the definitions of matroid.