Journal of Zhejiang University SCIENCE
(ISSN 1009-3095, Monthly)

2004   Vol. 5   No. 7   p.810-815


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

DAI Jian-hua*, CHEN Wei-dong, PAN Yun-he

(Institute of Artificial Intelligence, Zhejiang University, Hangzhou 310027, China)
*E-mail: jhdai@126.com
Received Nov. 5, 2003; revision accepted Feb. 27, 2004

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 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.

Key words: Rough set theory, Quasi-ordering, Axioms, Minimization
Document code: A           CLC number: TP18

References:

[1] Lin, T.Y., Liu, Q., 1994. Rough Approximate Operators: Axiomatic Rough Set Theory. In: Ziarko, W.P. (eds.), Proc. of Rough Sets, Fuzzy Sets and Knowledge Discovery. Springer-Verlag, London, p.256-260.

[2] Pawlak, Z., 1991. Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht.

[3] Pawlak, Z., Grzymala-Busse, J., Slowinski, R., Ziarko, W., 1995. Rough sets. Communications of the ACM, 38(11):89-95.

[4] Sun, H., Liu, D.Y., Li, W., 2002. The minimization of axiom groups of rough set. Chinese Journal of Computers, 25(2):202-209 (in Chinese).

[5] Yao, Y.Y., Wong, S.K.M., Lin, T.Y., 1997. A Review of Rough Set Models. In: Lin T.Y. and Cercone N. (eds.), Rough Sets and Data Mining: Analysis for Imprecise Data. Kluwer Academic Publishers, Boston, p.47-75.

[6] Yao, Y.Y., 1998a. Constructive and algebraic methods of the theory of rough sets. Information Sciences, 109(1-4):21-47.

[7] Yao, Y.Y., 1998b. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences, 111(1-4):239-259.

[8] Zhu, F., He, H.C., 2000. The axiomatization of the rough set. Chinese Journal of Computers, 23(3):330-333 (in Chinese).