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A Weakened Notion of Congruence to Reduce Concept Lattices

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Computational Intelligence and Mathematics for Tackling Complex Problems 2

Part of the book series: Studies in Computational Intelligence ((SCI,volume 955))

Abstract

This paper addresses the problem of attribute and size reduction of concept lattices in formal concept analysis. The reduction of the number of attributes in a formal context produces a partition on the set of concepts of the concept lattice. In this work, we introduce a weaker notion of congruence relation, called local congruence. This less restrictive kind of congruence guarantees that each subset of the partition forms a closed algebraic substructure, aggregating as few concepts as possible and preserving the main information.

Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (FEDER) project TIN2016-76653-P.

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Author information

Authors and Affiliations

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

    Roberto G. Aragón, Jesús Medina & Eloísa Ramírez-Poussa

Authors
  1. Roberto G. Aragón
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  2. Jesús Medina
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  3. Eloísa Ramírez-Poussa
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Corresponding author

Correspondence to Roberto G. Aragón .

Editor information

Editors and Affiliations

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

    María Eugenia Cornejo

  2. Faculty of Engineering Sciences, Széchenyi István University, Gyõr, Hungary

    László T. Kóczy

  3. Science Faculty, Department of Mathematics, University of Cádiz, Cádiz, Spain

    Jesús Medina-Moreno

  4. Escuela de Ingeniería Industrial, Universidad de Castilla La Mancha, Toledo, Spain

    Juan Moreno-García

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Aragón, R.G., Medina, J., Ramírez-Poussa, E. (2022). A Weakened Notion of Congruence to Reduce Concept Lattices. In: Cornejo, M.E., Kóczy, L.T., Medina-Moreno, J., Moreno-García, J. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems 2. Studies in Computational Intelligence, vol 955. Springer, Cham. https://doi.org/10.1007/978-3-030-88817-6_16

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