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Selected Properties of Generalized Hypothetical Syllogism Including the Case of R-implications

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

Abstract

In this paper we investigate the generalized hypothetical syllogism (GHS) in fuzzy logic, which can be seen as the functional equation \(\sup _{z\in [0,1]} T(I(x,z), I(z,y))=I(x,y)\), where I is a fuzzy implication and T is a t-norm. Our contribution is inspired by the article [Fuzzy Sets Syst 323:117–137 (2017)], where the author considered (GHS) when T is the minimum t-norm. We show several general results and then we focus on R-implications. We characterize all t-norms which satisfy (GHS) with arbitrarily fixed R-implication generated from a left-continuous t-norm.

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Acknowledgment

This work has been supported by the National Science Centre, Poland, through Project Number 2015/19/B/ST6/03259.

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Authors and Affiliations

  1. Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland

    Michał Baczyński & Katarzyna Miś

Authors
  1. Michał Baczyński
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  2. Katarzyna Miś
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Corresponding author

Correspondence to Michał Baczyński .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Baczyński, M., Miś, K. (2018). Selected Properties of Generalized Hypothetical Syllogism Including the Case of R-implications. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_57

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_57

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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