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Construction of Fuzzy Implications from the Bandler-Kohout Subproduct

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1601))

Abstract

A \(\sup -T\) composition (where T is a triangular norm) of two fuzzy implications can be again a fuzzy implication. Motivated by this fact, in this contribution, we consider the Bandler-Kohout subproduct (BKS), which is a composition of fuzzy relations based on the infimum. We verify when such a composition of fuzzy connectives can provide a fuzzy implication and we investigate its properties. Further, we consider BKS as a method of constructing a new fuzzy implication from given t-norms or t-conorms. Moreover, we study essential properties of possibly built implications.

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Acknowledgment

The author would like to thank anonymous reviewers for their valuable comments and remarks.

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Authors and Affiliations

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

    Katarzyna Miś

Authors
  1. Katarzyna Miś
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Correspondence to Katarzyna Miś .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

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Miś, K. (2022). Construction of Fuzzy Implications from the Bandler-Kohout Subproduct. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_19

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08970-1

  • Online ISBN: 978-3-031-08971-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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