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Concept Lattices as a Reduction Tool for Fuzzy Relation Equations

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Graph-Based Representation and Reasoning (ICCS 2023)

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Abstract

Recently, a procedure to reduce multi-adjoint relation equations has been published. Such method relies on the strong existing link between fuzzy relation equations and concept lattices, and more specifically, it is based on attribute reduction techniques. In this paper, we illustrate the reduction mechanism for the specific case of fuzzy relation equations on a more general structure than a residuated lattice, in which an adjoint triple is considered instead of a left continuous t-norm and its residuated implication.

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Acknowledgements

Partially supported by the 2014–2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in projects PID2019-108991GB-I00 and PID2022-137620NB-I00, with the Ecological and Digital Transition Projects 2021 of the Ministry of Science and Innovation in project TED2021-129748B-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA17124.

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Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, Cádiz, Spain

    David Lobo, Víctor López-Marchante & Jesús Medina

Authors
  1. David Lobo
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  2. Víctor López-Marchante
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  3. Jesús Medina
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Correspondence to David Lobo .

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Editors and Affiliations

  1. Universidad de Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  2. FernUniversität in Hagen, Hagen, Germany

    Kai Sauerwald

  3. Humboldt-Universität zu Berlin, Berlin, Germany

    Robert Jäschke

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Lobo, D., López-Marchante, V., Medina, J. (2023). Concept Lattices as a Reduction Tool for Fuzzy Relation Equations. In: Ojeda-Aciego, M., Sauerwald, K., Jäschke, R. (eds) Graph-Based Representation and Reasoning. ICCS 2023. Lecture Notes in Computer Science(). Springer, Cham. https://doi.org/10.1007/978-3-031-40960-8_17

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  • DOI: https://doi.org/10.1007/978-3-031-40960-8_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40959-2

  • Online ISBN: 978-3-031-40960-8

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