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Matroids and Submodular Functions for Covering-Based Rough Sets

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Uncertainty Management with Fuzzy and Rough Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 377))

Abstract

Covering-based rough set theory is an extension of Pawlak’s rough set theory, and it was proposed to expand the applications of the latter to more general contexts. In this case a covering is used instead of the partition obtained from an equivalence relation. Recently many authors have studied the relationships between covering-based rough sets, matroids and submodular functions. In this paper, we present the matroidal structures obtained from different partitions and coverings of a specific set. We also propose an extension of a matroidal structure for covering-based rough sets. Finally, we establish a partial order relation among the matroidal structures via submodular functions, coverings, and their approximation operators.

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Acknowledgements

This work was supported by the Universidad Militar Nueva Granada Special Research Fund, under the project CIAS 2549-2018.

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Authors and Affiliations

  1. Universidad Militar Nueva Granada, Bogotá, Colombia

    Mauricio Restrepo & John Fabio Aguilar

Authors
  1. Mauricio Restrepo
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  2. John Fabio Aguilar
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Corresponding author

Correspondence to Mauricio Restrepo .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Universidad Central "Marta Abreu" de Las Villas, Santa Clara, Villa Clara, Cuba

    Rafael Bello

  2. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Rafael Falcon

  3. Department of Computer Science and Artificial Intelligence, Technical School of Informatics and Telecommunications Engineering, University of Granada, Granada, Spain

    José Luis Verdegay

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Restrepo, M., Aguilar, J.F. (2019). Matroids and Submodular Functions for Covering-Based Rough Sets. In: Bello, R., Falcon, R., Verdegay, J. (eds) Uncertainty Management with Fuzzy and Rough Sets. Studies in Fuzziness and Soft Computing, vol 377. Springer, Cham. https://doi.org/10.1007/978-3-030-10463-4_10

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