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Fuzzy Multisets in Granular Hierarchical Structures Generated from Free Monoids

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Modeling Decisions for Artificial Intelligence (MDAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8234))

Abstract

This paper focuses on the two definitions of fuzzy multisets by Yager and Minamoto, respectively, and examines their difference in the framework of granular hierarchical structures generated from free monoids. Then we can conclude that, in order to define the basic order on the set of multisets on interval (0,1], the Yager definition adopts the one induced just from the range ℕ, the set of natural numbers, while the Miyamoto definition uses one generated from both the domain (0,1] and the range ℕ through the notion of cuts.

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Technologies, Hokkaido University, Japan

    Tetsuya Murai

  2. Graduate School of Systems and Information Engineering, University of Tsukuba, Japan

    Sadaaki Miyamoto

  3. Graduate School of Engineering Science, Osaka University, Japan

    Masahiro Inuiguchi

  4. College of Information and Systems, Muroran Institute of Technology, Japan

    Yasuo Kudo

  5. C-Republic, Japan

    Seiki Akama

Authors
  1. Tetsuya Murai
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  2. Sadaaki Miyamoto
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  3. Masahiro Inuiguchi
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  4. Yasuo Kudo
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  5. Seiki Akama
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Editor information

Editors and Affiliations

  1. IIIA-CSIC, Campüus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10, Naka, 186-0004, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Departament d’Enginyeria de la Informació i de les Comunicacions, Universitat Autonoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    Guillermo Navarro-Arribas

  4. Internet Interdisciplinary Institute (IN3); Estudis d’Informàtica, Multimèdia i Telecomunicació, Universitat Oberta de Catalunya, Rambla del Poblenou, 156, 08018, Barcelona, Catalonia, Spain

    David Megías

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Murai, T., Miyamoto, S., Inuiguchi, M., Kudo, Y., Akama, S. (2013). Fuzzy Multisets in Granular Hierarchical Structures Generated from Free Monoids. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Megías, D. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2013. Lecture Notes in Computer Science(), vol 8234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41550-0_22

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  • DOI: https://doi.org/10.1007/978-3-642-41550-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41549-4

  • Online ISBN: 978-3-642-41550-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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