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Bipartite Graphs and Coverings

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Rough Sets and Knowledge Technology (RSKT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6954))

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Abstract

In many real world applications, data are organized by coverings, instead of partitions. Covering-based rough sets have been proposed to cope with this type of data. Covering-based rough set theory is more general than rough set theory, then there is a need to employ sophisticated theories to make it more adaptive to applications. Covering is one of core concepts in covering-based rough sets, and it is urgent to connect coverings with other data models. This paper establishes the relationship between coverings and bipartite graphs. Through its index set, a covering induces some isomorphic bipartite graphs. Conversely, a bipartite graph induces a covering of the set of vertices. These inductions are converse with each other.

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References

  1. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  2. Liu, G., Sai, Y.: A comparison of two types of rough sets induced by coverings. International Journal of Approximate Reasoning 50, 521–528 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Tsang, E.C., Chen, D., Yeung, D.S.: Approximations and reducts with covering generalized rough sets. Computers & Mathematics with Applications 56, 279–289 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang, S., Zhu, P., Zhu, W.: Structure of covering-based rough sets. International Journal of Mathematical and Computer Sciences 6, 147–150 (2010)

    Google Scholar 

  5. Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Information Sciences 179, 210–225 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, D., Wang, C., Hu, Q.: A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Information Sciences 177, 3500–3518 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Deng, T., Chen, Y., Xu, W., Dai, Q.: A novel approach to fuzzy rough sets based on a fuzzy covering. Information Sciences 177, 2308–2326 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Qiu, W., Luo, Z.: Some results on fined covering fuzzy generalized rough sets. Computer Engineering and Applications 14, 86–88 (2006)

    Google Scholar 

  9. Zhu, W.: Relationship among basic concepts in covering-based rough sets. Information Sciences 17, 2478–2486 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhu, W., Wang, F.: On three types of covering rough sets. IEEE Transactions on Knowledge and Data Engineering 19, 1131–1144 (2007)

    Article  Google Scholar 

  11. Bartol, W., Miro, J., Pioro, K., Rossello, F.: On the coverings by tolerance classes. Information Sciences 166, 193–211 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, S., Zhu, W.: Matroidal structure of covering-based rough sets through the upper approximation number. To Appear in International Journal of Granular Computing, Rough Sets and Intelligent Systems (2011)

    Google Scholar 

  13. Zhu, W., Wang, F.: Reduction and axiomization of covering generalized rough sets. Information Sciences 152, 217–230 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhu, W., Wang, S.: Matroidal approaches to generalized rough sets based on relations. To Appear in International Journal of Machine Learning and Cybernetics (2011)

    Google Scholar 

  15. Zhu, W.: Topological approaches to covering rough sets. Information Sciences 177, 1499–1508 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bianucci, D., Cattaneo, G., Ciucci, D.: Entropies and co-entropies of coverings with application to incomplete information systems. Fundamenta Informaticae 75, 77–105 (2007)

    MathSciNet  MATH  Google Scholar 

  17. Li, F., Yin, Y.: Approaches to knowledge reduction of covering decision systems based on information theory. Information Sciences 179, 1694–1704 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Dash, M., Liu, H.: Consistency-based search in feature selection. Artificial Intelligence 151, 155–176 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Min, F., He, H., Qian, Y., Zhu, W.: Test-cost-sensitive attribute reduction. To Appear in Information Sciences (2011)

    Google Scholar 

  20. West, D.B.: Introduction to graph theory. Pearson Education, London (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Shiping Wang

  2. Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou, China

    William Zhu & Fan Min

Authors
  1. Shiping Wang
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  2. William Zhu
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  3. Fan Min
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, S4S 0A2, Saskatchewan, Canada

    JingTao Yao

  2. Department of Applied Computer Science, University of Winnipeg, R3B 2E9, Winnipeg, Canada

    Sheela Ramanna

  3. Institute of Computer Science & Technology, Chongqing University of Posts and Telecommunications, 400065, Chongqing, P.R. China

    Guoyin Wang

  4. Chair of Computer Science, University of Rzeszów, Poland

    Zbigniew Suraj

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© 2011 Springer-Verlag Berlin Heidelberg

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Wang, S., Zhu, W., Min, F. (2011). Bipartite Graphs and Coverings. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_90

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  • DOI: https://doi.org/10.1007/978-3-642-24425-4_90

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24424-7

  • Online ISBN: 978-3-642-24425-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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