相似关系粗糙集理论的一个极小公理组

A New Minimal Axiom Group of Rough Set Based on Similar Relation

粗糙集公理化是粗糙集理论研究的一个重要部分,其目的是用可靠且独立的公理组对粗糙集理论进行刻画,从而可以用逻辑和公理系统方法对粗糙集理论进行更为深入的研究.经典的粗糙集理论是基于等价关系的,但现实数据中存在更多的相似关系.为刻画基于相似关系粗糙集理论,给出了公理组S,它含有3个公理.证明了公理组的可靠性,它表明了用所给公理组刻画基于相似关系粗糙集理论的合理性.同时还证明了公理组的极小性,即公理组中每条公理是粗糙不等式且各公理是相互独立的.这些研究有助于粗糙集理论研究的深入和完善.

Rough set axiomatization is one aspect of rough set study,and the purpose is 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 classic rough set theory is based on equivalent relation,but rough set theory based on similar relation has wide applications in real world. To characterize similar 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 similar relation is rational,is proved. Simultaneously,the minimization of the axiom group,which requests that each axiom is an equation and each is independent,is proved. The axiom group is helpful to research rough set theory by logic and axiom system methods.