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On Fuzzy Rough Set Algebras in Infinite Universes

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Rough Sets and Knowledge Technology (RSKT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5589))

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Abstract

A fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a fuzzy/crist set in a fuzzy approximation space. A fuzzy rough set algebra is a fuzzy set algebra with added dual pair of fuzzy rough approximation operators. In this paper, we study the mathematical structures of fuzzy rough set algebras in infinite universes of discourse. We first define the concept of fuzzy rough set algebras by the axiomatic approach. We then examine the properties of fuzzy rough approximation operators in different types of fuzzy rough set algebras. We also prove that if a system \(({\cal F}(U), \cap, \cup, \sim, L, H)\) is a (respectively, a serial, a reflexive, a symmetric, a transitive, a topological, a similarity) fuzzy rough set algebra then the derived system \(({\cal F}(U), \cap, \cup, \sim, LL, HH)\) is also a (respectively, a serial, a reflexive, a symmetric, a transitive, a topological, a similarity) fuzzy rough set algebra.

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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. Faculty of Engineering and Surveying and Engineering, University of Southern Queensland, QLD 4350, Australia

    Peng Wen

  2. School of Information Technology, Queensland University of Technology, QLD 4001, Brisbane, Australia

    Yuefeng Li

  3. Institute of Mathematics, Warsaw University of Technology, Koszykowa 86, 02008, Warsaw, Poland

    Lech Polkowski

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  5. Faculty of Medicine, Department of Medical Informatics, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shusaku Tsumoto

  6. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

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© 2009 Springer-Verlag Berlin Heidelberg

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Wu, WZ., Xu, YH. (2009). On Fuzzy Rough Set Algebras in Infinite Universes. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds) Rough Sets and Knowledge Technology. RSKT 2009. Lecture Notes in Computer Science(), vol 5589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02962-2_39

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  • DOI: https://doi.org/10.1007/978-3-642-02962-2_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02961-5

  • Online ISBN: 978-3-642-02962-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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