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From Semi-fuzzy to Fuzzy Quantifiers via Łukasiewicz Logic and Games

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 641))

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Abstract

Various challenges for lifting semi-fuzzy quantifier models to fully fuzzy ones are discussed. The aim is to embed such models into Łukasiewicz logic in a systematic manner. Corresponding extensions of Giles’ game with random choices of constants as well as precisifications of fuzzy models are introduced for this purpose.

Work supported by the Austrian Science Fund (FWF) project FWF I1897-N25.

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Notes

  1. 1.

    For convenience, we identify constant symbols with domain elements.

  2. 2.

    In rival candidates, like Gödel logic or Product logic the truth function for implication is not continuous.

  3. 3.

    The payoff scheme may look arbitrary at a first glimpse. However it results from Giles’s interpretation of the truth value of a given atom A in terms of the expected loss for a player, who has to pay a fixed amount of money (say 1 Euro) to the opposing player, if a certain experiment \(E_A\) associated with A fails. Such (binary) experiments may show dispersion, i.e. repeated executions of the same experiment \(E_A\) may show different results. However for each A a fixed failure probability (risk) is associated to \(E_A\).

  4. 4.

    Note that, despite the fact that a precisification evaluates atomic formulas classically, the valuation under a precisification of a formula involving a semi-fuzzy quantifier might be an intermediate value in [0, 1].

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Authors and Affiliations

  1. TU Wien, Vienna, Austria

    Paolo Baldi & Christian G. Fermüller

Authors
  1. Paolo Baldi
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  2. Christian G. Fermüller
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Corresponding author

Correspondence to Paolo Baldi .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Sławomir Zadrożny

  4. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Baldi, P., Fermüller, C.G. (2018). From Semi-fuzzy to Fuzzy Quantifiers via Łukasiewicz Logic and Games. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-66830-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66829-1

  • Online ISBN: 978-3-319-66830-7

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