JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (08): 80-85.doi: 10.6040/j.issn.1671-9352.1.2014.009

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Matroidal structure of the upper approximation of covering-based rough set defined by the neighborhood

LI Qing-yin, ZHU William   

  1. Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, Fujian, China
  • Received:2014-06-02 Revised:2014-07-08 Published:2014-09-24

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Abstract: By neighborhoods, a matroidal structure of the upper approximation of covering-based rough sets is constructed. Through transversal theory and base axioms, the matroidal structure is established. By the lower approximations of the complementary neighborhood, a family related to neighborhoods is equivalent represented. Finally, a sufficient and necessary condition for the family to be the set of all hyperplanes of the matroid is studied from the viewpoint of cardinality.

Key words: hyperplane, neighborhood, matroid, base, covering, approximation operator

CLC Number: 

  • TP18
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