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Granularity and Approximation in Sequences, Multisets, and Sets in the Framework of Kripke Semantics

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Integrated Uncertainty Management and Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 68))

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Abstract

This paper makes some consideration on representing the concepts of sequences, multisets, and usual subsets in the framework of Kripke semantics. First, a Carnap model, which is a tuple of a non-empty set of possible worlds and a valuation mapping, that is, a Kripke model without a binary relation on the nonempty set, is shown to represent, in general, a multiset, and in special case, a subset. Also sequences and digital images are represented by special kinds of Kripke models. Further, when a binary relation on the non-empty set, two approximation operators can be defined.

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo, 060-0814, Japan

    Tetsuya Murai & Seiki Ubukata

  2. Department of Information Engineering, Muroran Institute of Technology, 27-1, Muroran, 050-8585, Japan

    Yasuo Kudo

  3. C-Republic, 1-20-1, Higashi-Yurigaoka, Asao-ku, Kawasaki, 215-0012, Japan

    Seiki Akama

  4. Department of Risk Engineering, University of Tsukuba, Ibaraki, 305-8573, Japan

    Sadaaki Miyamoto

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

Editors and Affiliations

  1. School of Knowledge Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, 923-1292, Ishikawa, Japan

    Van-Nam Huynh  & Yoshiteru Nakamori  & 

  2. Department of Engineering Mathematics, University of Bristol, Queen’s Building, University Walk, BS8 1TR, Bristol, United Kingdom

    Jonathan Lawry

  3. Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

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Murai, T., Ubukata, S., Kudo, Y., Akama, S., Miyamoto, S. (2010). Granularity and Approximation in Sequences, Multisets, and Sets in the Framework of Kripke Semantics. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_30

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  • DOI: https://doi.org/10.1007/978-3-642-11960-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11959-0

  • Online ISBN: 978-3-642-11960-6

  • eBook Packages: EngineeringEngineering (R0)

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