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Lattice Structures of Rough Fuzzy Sets

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Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5908))

Abstract

This paper studies lattice structure of the family of rough fuzzy sets in a given approximation space. Our result is an extension of standard rough sets. Starting with the definition of rough fuzzy sets, the union, intersection and pseudocomplementation operations are generalized. Then it is proved that the above family with these operations is a distributive lattice. This paper also gives the characterization of borderline region of rough fuzzy sets.

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Author information

Authors and Affiliations

  1. School of Information Science, Beijing Language and Culture University, Beijing, 100083, China

    Guilong Liu

Authors
  1. Guilong Liu
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Aided Sciences, Kyushu Institute of Technology, 804-8550, Tobata, Kitakyushu, Japan

    Hiroshi Sakai

  2. Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, 700019, Kolkata, India

    Mihir Kumar Chakraborty

  3. Information Technology Department, University of Cairo, 5 Ahmed Zewal St. Orman, Giza, Egypt

    Aboul Ella Hassanien

  4. University of Warsaw & Infobright Inc., Poland

    Dominik Ślęzak

  5. University of Electronic Science and Technology of China, Chengdu, China

    William Zhu

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© 2009 Springer-Verlag Berlin Heidelberg

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Liu, G. (2009). Lattice Structures of Rough Fuzzy Sets. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2009. Lecture Notes in Computer Science(), vol 5908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10646-0_31

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  • DOI: https://doi.org/10.1007/978-3-642-10646-0_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10645-3

  • Online ISBN: 978-3-642-10646-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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