Some minimal axiom sets of rough sets

The axiomatic approach is an important one to the development of rough set theory. This paper proposes some independent and minimal axiom sets for characterizing the classical rough set. First, we investigate the correlations among some arbitrary binary relations in rough sets. Then, we provide several forms of equivalence relations which are different from the original ones. Finally, to well characterize the classical rough set, we propose fifteen new minimal axiom sets of rough sets based on the new equivalence relations. By employing relative tables, the independence of axiom sets for characterizing the approximation operators is also examined.