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Received: 2003-11-05
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A minimal axiom group for rough set based on quasi-ordering
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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.
@article{title="A minimal axiom group for rough set based on quasi-ordering",
author="DAI Jian-hua, CHEN Wei-dong, PAN Yun-he",
journal="Journal of Zhejiang University Science A",
volume="5",
number="7",
pages="810-815",
year="2004",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2004.0810"
}
%0 Journal Article
%T A minimal axiom group for rough set based on quasi-ordering
%A DAI Jian-hua
%A CHEN Wei-dong
%A PAN Yun-he
%J Journal of Zhejiang University SCIENCE A
%V 5
%N 7
%P 810-815
%@ 1869-1951
%D 2004
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.0810
TY - JOUR
T1 - A minimal axiom group for rough set based on quasi-ordering
A1 - DAI Jian-hua
A1 - CHEN Wei-dong
A1 - PAN Yun-he
J0 - Journal of Zhejiang University Science A
VL - 5
IS - 7
SP - 810
EP - 815
%@ 1869-1951
Y1 - 2004
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.0810
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.
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