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The Semantics of Fuzzy Logics: Two Approaches to Finite Tomonoids

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 336))

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Abstract

Fuzzy logic generalises classical logic; in addition to the latter’s truth values “false” and “true”, the former allows also intermediary truth degrees. The conjunction is, accordingly, interpreted by an operation acting on a chain, making the set of truth degrees into a totally ordered monoid. We present in this chapter two different ways of investigating this type of algebras. We restrict to the finite case.

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Acknowledgments

The support of the first author by the Austrian Science Fund (FWF): project I 1923-N25 (New perspectives on residuated posets) and the support of the second author by the Czech Science Foundation under Project 15-07724Y are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria

    Thomas Vetterlein

  2. Department of Mathematics Faculty of Engineering, Czech University of Life Sciences, Prague, Czech Republic

    Milan Petrík

Authors
  1. Thomas Vetterlein
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  2. Milan Petrík
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Correspondence to Thomas Vetterlein .

Editor information

Editors and Affiliations

  1. Dept of Knowledge-Based Math. Systems, Johannes Kepler University Linz, Linz, Austria

    Susanne Saminger-Platz

  2. Dept. of Mathematics & Descriptive Geo., Slovak University of Technology, BRATISLAVA, Slovakia

    Radko Mesiar

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Vetterlein, T., Petrík, M. (2016). The Semantics of Fuzzy Logics: Two Approaches to Finite Tomonoids. In: Saminger-Platz, S., Mesiar, R. (eds) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-319-28808-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-28808-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28807-9

  • Online ISBN: 978-3-319-28808-6

  • eBook Packages: EngineeringEngineering (R0)

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