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Similarity of binary relations based on rough set theory and topology: an application for topological structures of matroids

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Abstract

In this paper, we propose an integration of rough sets, matroids and topology to exploit the advantages of three theories. First, we consider topologies induced by binary relations and illustrate that binary relations can be researched by means of topology. Next, similarity of binary relations based on rough set theory and topology is introduced and the fact that every binary relation is solely similar to some preorder relation is proved. Finally, as an application of the similarity, topological structures of matroids are given.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the quality of the paper. This work is supported by NSF of China (11261005, 11161029, 11461002, 11461005), NSF of Guangxi (2012GXNSFDA276040, 2014GXNSFAA118001), NSF for Young Scholar of Guangxi (2013GXNSFBA019020), Guangxi Province Universities and Colleges Excellence Scholar and Innovation Team Funded Scheme, Key Discipline of Quantitative Economics in Guangxi Univresity of Finance and Economics (2014YBKT07) and Quantitative Economics Key Laboratory Program of Guangxi University of Finance and Economics (2014SYS01).

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Authors and Affiliations

  1. School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, 530003, Guangxi, People’s Republic of China

    Bin Qin & Kesong Yan

  2. Department of Academic Affairs, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, People’s Republic of China

    Guoen Xia

Authors
  1. Bin Qin
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  2. Guoen Xia
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  3. Kesong Yan
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Correspondence to Bin Qin.

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Communicated by A. Di Nola.

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Qin, B., Xia, G. & Yan, K. Similarity of binary relations based on rough set theory and topology: an application for topological structures of matroids. Soft Comput 20, 853–861 (2016). https://doi.org/10.1007/s00500-015-1846-7

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  • DOI: https://doi.org/10.1007/s00500-015-1846-7

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