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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This work was supported by the Universidad Militar Nueva Granada Special Research Fund, under the project CIAS 2549-2018.
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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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DOI: https://doi.org/10.1007/978-3-030-10463-4_10
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