Minimal axiom group of similarity-based rough set model

Abstract

Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. The classical rough set theory is based on equivalence relation, but the rough set theory based on similarity relation has wide applications in the real world. To characterize similarity-based rough set theory, an axiom group named S, consisting of 3 axioms, is proposed. The reliability of the axiom group, which shows that characterizing of rough set theory based on similarity relation is rational, is proved. Simultaneously, the minimization of the axiom group, which requests that each axiom is an equation and independent, is proved. The axiom group is helpful to research rough set theory by logic and axiom system methods.