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Journal of Applied Mathematics
Volume 2012, Article ID 236307, 25 pages
http://dx.doi.org/10.1155/2012/236307
Research Article

Geometric Lattice Structure of Covering-Based Rough Sets through Matroids

Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, China

Received 26 August 2012; Accepted 21 November 2012

Academic Editor: Zhijun Liu

Copyright © 2012 Aiping Huang and William Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • Aiping Huang, Hong Zhao, and William Zhu, “Nullity-based Matroid of Rough Sets and Its Application to Attribute Reduction,” Information Sciences, 2013. View at Publisher · View at Google Scholar
  • Yanfang Liu, and William Zhu, “Comparative study between extension of covering approximation space and its induction through transversal matroid,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8170, pp. 225–235, 2013. View at Publisher · View at Google Scholar
  • Hua Yao, and William Zhu, “Applications of repeat degree to coverings of neighborhoods,” International Journal of Machine Learning and Cybernetics, 2014. View at Publisher · View at Google Scholar
  • Lirun Su, and William Zhu, “Closed-set lattice and modular matroid induced by covering-based rough sets,” International Journal of Machine Learning and Cybernetics, 2014. View at Publisher · View at Google Scholar
  • Aiping Huang, and William Zhu, “Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids,” Journal of Applied Mathematics, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • Aiping Huang, and William Zhu, “Connectedness of graphs and its application to connected matroids through covering-based rough sets,” Soft Computing, 2015. View at Publisher · View at Google Scholar
  • Yanfang Liu, Hong Zhao, and William Zhu, “Parametric Matroid of Rough Set,” International Journal Of Uncertainty Fuzziness And Knowledge-Based Systems, vol. 23, no. 6, pp. 893–908, 2015. View at Publisher · View at Google Scholar
  • Guoye Xu, and Zhaohao Wang, “A rough set approach to the characterization of transversal matroids,” International Journal Of Approximate Reasoning, vol. 70, pp. 1–12, 2016. View at Publisher · View at Google Scholar
  • Aiping Huang, and William Zhu, “Characteristic matrices of compound operations of coverings and their relationships with rough sets,” International Journal of Machine Learning and Cybernetics, vol. 10, no. 1, pp. 75–85, 2019. View at Publisher · View at Google Scholar
  • Mauricio Restrepo, and John Fabio Aguilar, “Matroids and submodular functions for covering-based rough sets,” Studies in Fuzziness and Soft Computing, vol. 377, pp. 175–191, 2019. View at Publisher · View at Google Scholar