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On Fuzzy Topological Structures of Rough Fuzzy Sets

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Transactions on Rough Sets XVI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 7736))

Abstract

A rough fuzzy set is the result of approximation of a fuzzy set with respect to a crisp approximation space. In this paper, we investigate topological structures of rough fuzzy sets. We first show that a reflexive crisp rough approximation space can induce a fuzzy Alexandrov space. We then prove that the lower and upper rough fuzzy approximation operators are, respectively, the fuzzy interior operator and fuzzy closure operator if and only if the binary relation in the crisp approximation space is reflexive and transitive. We also examine that a similarity crisp approximation space can produce a fuzzy clopen topological space. Finally, we present the sufficient and necessary conditions that a fuzzy interior (closure, respectively) operator derived from a fuzzy topological space can associate with a reflexive and transitive crisp relation such that the induced lower (upper, respectively) rough fuzzy approximation operator is exactly the fuzzy interior (closure, respectively) operator.

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Author information

Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, P.R. China

    Wei-Zhi Wu & You-Hong Xu

Authors
  1. Wei-Zhi Wu
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  2. You-Hong Xu
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Editor information

Editors and Affiliations

  1. University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

  2. University of Warsaw, Poland

    Andrzej Skowron

  3. University of Winnipeg, MB, Canada

    Sheela Ramanna

  4. University of Rzeszów, Poland

    Zbigniew Suraj

  5. University of Calgary, AB, Canada

    Xin Wang

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Wu, WZ., Xu, YH. (2013). On Fuzzy Topological Structures of Rough Fuzzy Sets. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds) Transactions on Rough Sets XVI. Lecture Notes in Computer Science, vol 7736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36505-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-36505-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36504-1

  • Online ISBN: 978-3-642-36505-8

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