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Approximating Fuzzy Relation Equations Through Concept Lattices

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Formal Concept Analysis (ICFCA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13934))

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Abstract

Fuzzy relation equations (FRE) is a formal theory broadly studied in the literature and applied to decision making, optimization problems, image processing, etc. It is usual that the initial data contains uncertain, imperfect or incomplete information, which can imply, for instance, the existence of inconsistencies. As a consequence, the FRE that arises from the data may be unsolvable. Taking advantage of the relationship between FRE and concept lattices, this paper is focused on three mechanisms for approximating unsolvable FRE. Several properties have been introduced and different distances for determining the best approximation are considered and applied to an example.

Partially supported by the 2014–2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in project PID2019-108991GB-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 Jesús Medina .

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Editors and Affiliations

  1. Universität Kassel, Kassel, Germany

    Dominik Dürrschnabel

  2. Universidad de Málaga, Málaga, Spain

    Domingo López Rodríguez

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Lobo, D., López-Marchante, V., Medina, J. (2023). Approximating Fuzzy Relation Equations Through Concept Lattices. In: Dürrschnabel, D., López Rodríguez, D. (eds) Formal Concept Analysis. ICFCA 2023. Lecture Notes in Computer Science(), vol 13934. Springer, Cham. https://doi.org/10.1007/978-3-031-35949-1_1

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  • DOI: https://doi.org/10.1007/978-3-031-35949-1_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-35948-4

  • Online ISBN: 978-3-031-35949-1

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