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Fuzzy Sets, Multisets, and Rough Approximations

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9376))

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Abstract

Multisets alias bags are similar to fuzzy sets but essentially different in basic concepts and operations. We overview multisets together with basics of fuzzy sets in order to observe differences between the two. We then introduce fuzzy multisets and the combination of the both concepts. There is another concept of real-valued multisets as a generalization of multisets. Rough approximations of multisets and fuzzy multisets are discussed which uses a natural projection of the universal set onto the set of equivalence classes.

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References

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Author information

Authors and Affiliations

  1. Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Sadaaki Miyamoto

Authors
  1. Sadaaki Miyamoto
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Correspondence to Sadaaki Miyamoto .

Editor information

Editors and Affiliations

  1. Science and Technology, Japan Advanced Institute of, Nomi, Japan

    Van-Nam Huynh

  2. Science, Dept of Systems Innovation, Osaka University,Graduate School of, Osaka, Japan

    Masahiro Inuiguchi

  3. Université de Technologie de Compiègne, Compiègne, France

    Thierry Demoeux

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© 2015 Springer International Publishing Switzerland

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Miyamoto, S. (2015). Fuzzy Sets, Multisets, and Rough Approximations. In: Huynh, VN., Inuiguchi, M., Demoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science(), vol 9376. Springer, Cham. https://doi.org/10.1007/978-3-319-25135-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-25135-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25134-9

  • Online ISBN: 978-3-319-25135-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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