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Topological Residuated Lattice: A Unifying Algebra Representation of Some Rough Set Models

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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

As a unifying algebra representation of some rough set models (include Pawlak standard rough set, (I, T)-fuzzy rough set, residuated lattice based fuzzy rough set and intuitionistic fuzzy rough set), a new notion of the topological residuated lattice is introduced, and its basic properties are given. Moreover, the relationship between topological residuated lattice and triangle algebra are investigated.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ningbo University, Ningbo 315211, Zhejiang Province, P.R. China

    Xiaohong Zhang

Authors
  1. Xiaohong Zhang
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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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Zhang, X. (2009). Topological Residuated Lattice: A Unifying Algebra Representation of Some Rough Set Models. 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_13

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  • DOI: https://doi.org/10.1007/978-3-642-02962-2_13

  • 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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