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International Joint Conference on Rough Sets

IJCRS 2017: Rough Sets pp 154–164Cite as

Approximation Operators in Covering Based Rough Sets from Submodular Functions

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10313))

Abstract

We present a new collection of upper approximation operators for covering based rough sets, obtained from sub modular functions and closure operators. Each non decreasing submodular function defines a closure operator that can be considered as an approximation operator. The construction allows us to define several upper approximation operators. Some properties of these operators are studied.

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References

  1. Bian, X., Wang, P., Yu, Z., Bai, X., Chen, B.: Characterization of coverings for upper approximation operators being closure operators. Inf. Sci. 314, 41–54 (2015)

    Article  MathSciNet  Google Scholar 

  2. Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer Universitext, London (2005)

    MATH  Google Scholar 

  3. Deer, L., Restrepo, M., Cornelis, C., Gómez, J.: Neighborhood operators for covering-based rough sets. Inf. Sci. 336, 21–44 (2016)

    Article  Google Scholar 

  4. Li, X., Liu, S.: Matroidal approaches to rough sets via closure operators. Int. J. Approx. Reason. 53, 513–527 (2012)

    Article  MathSciNet  Google Scholar 

  5. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982)

    Article  Google Scholar 

  6. Pomykala, J.A.: Approximation operations in approximation space. Bulletin de la Académie Polonaise des Sciences 35(9–10), 653–662 (1987)

    MathSciNet  MATH  Google Scholar 

  7. Restrepo, M., Cornelis, C., Gómez, J.: Duality, conjugacy and adjointness of approximation operators in covering-based rough sets. Int. J. Approx. Reason. 55, 469–485 (2014)

    Article  MathSciNet  Google Scholar 

  8. Restrepo, M., Cornelis, C., Gómez, J.: Partial order relation for approximation operators in covering-based rough sets. Inf. Sci. 284, 44–59 (2014)

    Article  MathSciNet  Google Scholar 

  9. Roa, L.: Una nueva construcción de los espacios topológicos finitos desde las funciones submodulares. Tesis de Maestría en Matemáticas. Universidad Nacional de Colombia, Bogotá (2012)

    Google Scholar 

  10. Tang, J., She, K., Min, F., Zhu, W.: A matroidal approach to rough set theory. Theoret. Comput. Sci. 47(1), 1–11 (2013)

    Article  MathSciNet  Google Scholar 

  11. Tsang, E., Chen, D., Lee, J., Yeung, D.S.: On the upper approximations of covering generalized rough sets. In: Proceedings of the 3rd International Conference on Machine Learning and Cybernetics, pp. 4200–4203 (2004)

    Google Scholar 

  12. Varela, R.: FD- Relaciones. Tesis de Maestría en Matemáticas. Universidad Nacional de Colombia, Bogotá (2011)

    Google Scholar 

  13. Wang, S., Zhu, W., Min, F.: Transversal and function matroidal structures of covering-based rough sets. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 146–155. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24425-4_21

    Chapter  Google Scholar 

  14. Wu, M., Wu, X., Shen, T.: A new type of covering approximation operators. In: IEEE International Conference on Electronic Computer Technology, pp. 334–338 (2009)

    Google Scholar 

  15. Xu, Z., Wang, Q.: On the properties of covering rough sets model. J. Henan Normal Univ. (Nat. Sci.) 33(1), 130–132 (2005)

    MathSciNet  MATH  Google Scholar 

  16. Yang, T., Li, Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approx. Reason. 51, 335–345 (2010)

    Article  MathSciNet  Google Scholar 

  17. Liu, Y., Zhu, W.: Relation matroid and its relationship with generalized rough set based on relations. CoRR abs 1209.5456 (2012)

    Google Scholar 

  18. Liu, Y., Zhu, W., Zhang, Y.: Relationship between partition matroids and rough sets through \(k\)-rank matroids. J. Inf. Comput. Sci. 8, 2151–2163 (2012)

    Google Scholar 

  19. Li, Y., Wang, Z.: The relationships between degree rough sets and matroids. Anals Fuzzy Math. Inform. 12(1), 139–153 (2012)

    MathSciNet  MATH  Google Scholar 

  20. Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Inf. Sci. 109, 21–47 (1998)

    Article  MathSciNet  Google Scholar 

  21. Yao, Y.Y., Yao, B.: Covering based rough sets approximations. Inf. Sci. 200, 91–107 (2012)

    Article  MathSciNet  Google Scholar 

  22. Zakowski, W.: Approximations in the space \((u,\pi )\). Demonstr. Math. 16, 761–769 (1983)

    MATH  Google Scholar 

  23. Zhao, Z.: On some types of covering rough sets from topological points of view. Int. J. Approx. Reason. 68, 1–14 (2016)

    Article  MathSciNet  Google Scholar 

  24. Zhu, W.: Properties of the first type of covering-based rough sets. In: Proceedings of Sixth IEEE International Conference on Data Mining - Workshops, pp. 407–411 (2006)

    Google Scholar 

  25. Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)

    Article  MathSciNet  Google Scholar 

  26. Zhu, W., Wang, F.: A new type of covering rough set. In: Proceedings of Third International IEEE Conference on Intelligence Systems, pp. 444–449 (2006)

    Google Scholar 

  27. Zhu, X.Z., Zhu, W., Fan, X.N.: Rough sets methods in features selection via submodular function. Soft Comput. 21, 3699–3711 (2017)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Universidad Militar Nueva Granada, Bogotá, Colombia

    Mauricio Restrepo

Authors
  1. Mauricio Restrepo
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Corresponding author

Correspondence to Mauricio Restrepo .

Editor information

Editors and Affiliations

  1. Polish-Japanese Academy of Information Technology, Warsaw, Poland

    Lech Polkowski

  2. University of Regina, Regina, SK, Canada

    Yiyu Yao

  3. University of Warmia and Mazury, Olsztyn, Poland

    Piotr Artiemjew

  4. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  5. Southwest Jiaotong University, Chengdu, China

    Dun Liu

  6. Warsaw University, Warszawa, Poland

    Dominik Ślęzak

  7. Silesian University, Sosnowiec, Poland

    Beata Zielosko

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Restrepo, M. (2017). Approximation Operators in Covering Based Rough Sets from Submodular Functions. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-60837-2_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60836-5

  • Online ISBN: 978-3-319-60837-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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