On rough fuzzy set algebras

  • Authors:

  • Wei-Zhi Wu;You-Hong Xu

  • Affiliations:

  • Information College, Zhejiang Ocean University, Zhoushan, Zhejiang, P. R. China;Information College, Zhejiang Ocean University, Zhoushan, Zhejiang, P. R. China

  • Venue:
  • FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
  • Year:
  • 2006

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Abstract

A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space. A rough fuzzy set algebra is a fuzzy set algebra with added dual pair of rough fuzzy approximation operators. In this paper, structures of rough fuzzy set algebras are studied. It is proved that if a system $({\cal F}(U), \cap, \cup, \sim, L, H)$ is a (a serial, a reflexive, a symmetric, a transitive, an Euclidean, a Pawlak, respectively) rough fuzzy set algebra then the derived system $({\cal F}(U), \cap, \cup, \sim, LL, HH)$ is a (a serial, a reflexive, a symmetric, a transitive, an Euclidean, a Pawlak, respectively) rough fuzzy set algebra. Properties of rough fuzzy approximation operators in different types of rough fuzzy set algebras are also examined.