Topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets

  • Authors:

  • Zhen Ming Ma;Bao Qing Hu

  • Affiliations:

  • School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China and School of Science, Linyi University, Linyi 276005, PR China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2013

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Abstract

This paper builds the topological and lattice structures of L-fuzzy rough sets by introducing lower and upper sets. In particular, it is shown that when the L-relation is reflexive, the upper (resp. lower) set is equivalent to the lower (resp. upper) L-fuzzy approximation set. Then by the upper (resp. lower) set, it is indicated that an L-preorder is the equivalence condition under which the set of all the lower (resp. upper) L-fuzzy approximation sets and the Alexandrov L-topology are identical. However, associating with an L-preorder, the equivalence condition that L-interior (resp. closure) operator accords with the lower (resp. upper) L-fuzzy approximation operator is investigated. At last, it is proven that the set of all the lower (resp. upper) L-fuzzy approximation sets forms a complete lattice when the L-relation is reflexive.