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Rough 3-Valued Łukasiewicz Agebras and MV-Algebras

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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

Many researchers study rough sets from the point of view of description of the rough set pairs(a rough set pair is also called a rough set), i.e. 〈lower approximation set, upper approximation set〉. Dai [4] showed that all the rough sets in an approximation space constructs a 3-valued Łukasiewicz algebra. The constructed algebra is called the rough 3-valued Łukasiewicz algebra. It is shown that a rough 3-valued Łukasiewicz algebra is an MV-algbra in this paper. The direct relation between rough set theory and MV-algebras is constructed. The definition of rough MV-algebras is also given.

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Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Zhejiang University, Hangzhou, 310027, P.R. China

    Jianhua Dai & Xiaochun Liu

  2. Center for the Study of Language and Cognition, Zhejiang University, Hangzhou, 310028, P.R. China

    Jianhua Dai

  3. Qiushi Academy of Advanced Studies, Zhejiang University, Hangzhou, 310027, P.R. China

    Jianhua Dai & Xiaochun Liu

Authors
  1. Jianhua Dai
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  2. Xiaochun Liu
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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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Dai, J., Liu, X. (2009). Rough 3-Valued Łukasiewicz Agebras and MV-Algebras. 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_4

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  • DOI: https://doi.org/10.1007/978-3-642-02962-2_4

  • 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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