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On the Definition of Fuzzy Relational Galois Connections Between Fuzzy Transitive Digraphs

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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))

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Abstract

We continue the study of different generalizations of the notion of Galois connection. Previously, we had focused on the cases in which both the domain and codomain had the structure of either a transitive digraph or a fuzzy transitive digraph. Here, we extend it to the fuzzy relational framework. Specifically, we present a suitable notion of fuzzy relational Galois connection between fuzzy transitive digraphs where both components are now fuzzy relations and the underlying truth value algebra is a complete Heyting algebra. The resulting notion of fuzzy relational Galois connection inherits interesting characterisations of the notion of (crisp) relational Galois connection.

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Notes

  1. 1.

    For convenience, hereafter, we will always omit the prefix \(\mathbb L\).

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Acknowledgements

Partially supported by the Spanish Ministry of Science, Innovation, and Universities (MCIU), State Agency of Research (AEI), Junta de Andalucía (JA), Universidad de Málaga (UMA) and European Regional Development Fund (FEDER) through the projects PGC2018-095869-B-I00 and TIN2017-89023-P (MCIU/AEI/FEDER), and UMA2018-FEDERJA-001 (JA/UMA/FEDER).

Author information

Authors and Affiliations

  1. Departamento Matemática Aplicada, Universidad de Málaga, Málaga, Spain

    Inma P. Cabrera, Pablo Cordero, Emilio Muñoz-Velasco & Manuel Ojeda-Aciego

  2. KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Ghent, Belgium

    Bernard De Baets

Authors
  1. Inma P. Cabrera
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  2. Pablo Cordero
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  3. Emilio Muñoz-Velasco
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  4. Manuel Ojeda-Aciego
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  5. Bernard De Baets
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Corresponding author

Correspondence to Manuel Ojeda-Aciego .

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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Cabrera, I.P., Cordero, P., Muñoz-Velasco, E., Ojeda-Aciego, M., De Baets, B. (2022). On the Definition of Fuzzy Relational Galois Connections Between Fuzzy Transitive Digraphs. 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_9

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_9

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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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