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Construction of Associative Functions for Several Fuzzy Logics via the Ordinal Sum Theorem

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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))

Abstract

In this report, the ordinal sum theorem of semigroups is applied to construct logical operations for several fuzzy logics. The generalized form of ordinal sum for fuzzy logics on [0, 1] is defined in order to uniformly express several families of logical operations. Then, the conditions in ordinal sums for various properties of logical operations are presented: for examples, the monotonicity, the location of the unit element, the left/right-continuity, or and/or-likeness. Finally, some examples to construct pseudo-uninorms by the proposed method are illustrated.

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Author information

Authors and Affiliations

  1. Hokkaido University, Sapporo, 060-0814, Japan

    Mayuka F. Kawaguchi

  2. Tokyo Denki University, Inzai, Chiba, 270-1382, Japan

    Michiro Kondo

Authors
  1. Mayuka F. Kawaguchi
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  2. Michiro Kondo
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Corresponding author

Correspondence to Mayuka F. Kawaguchi .

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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Kawaguchi, M.F., Kondo, M. (2015). Construction of Associative Functions for Several Fuzzy Logics via the Ordinal Sum Theorem. 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_6

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  • DOI: https://doi.org/10.1007/978-3-319-25135-6_6

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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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