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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.7 P.810~815


A minimal axiom group for rough set based on quasi-ordering

Author(s):  DAI Jian-hua, CHEN Wei-dong, PAN Yun-he

Affiliation(s):  Institute of Artificial Intelligence, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   jhdai@126.com

Key Words:  Rough set theory, Quasi-ordering, Axioms, Minimization

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DAI Jian-hua, CHEN Wei-dong, PAN Yun-he. A minimal axiom group for rough set based on quasi-ordering[J]. Journal of Zhejiang University Science A, 2004, 5(7): 810~815.

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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 classic rough set theory is based on equivalent relation, but rough set theory based on reflexive and transitive relation (called quasi-ordering) has wide applications in the real world. To characterize topological rough set theory, an axiom group named RT, consisting of 4 axioms, is proposed. It is proved that the axiom group reliability in characterizing rough set theory based on similar relation is reasonable. Simultaneously, the minimization of the axiom group, which requires that each axiom is an equation and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods.

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