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Developing Complementary Rough Inclusion Functions Cover

Developing Complementary Rough Inclusion Functions

By: Adam Grabowski  
Open Access
|May 2020

References

  1. [1] Michel Marie Deza and Elena Deza. Encyclopedia of distances. Springer, 2009. doi:10.1007/978-3-642-30958-8.10.1007/978-3-642-30958-8
  2. [2] Anna Gomolińska. Rough approximation based on weak q-RIFs. In James F. Peters, Andrzej Skowron, Marcin Wolski, Mihir K. Chakraborty, and Wei-Zhi Wu, editors, Transactions on Rough Sets X, volume 5656 of Lecture Notes in Computer Science, pages 117–135, Berlin, Heidelberg, 2009. Springer. ISBN 978-3-642-03281-3. doi:10.1007/978-3-642-03281-3_4.10.1007/978-3-642-03281-3_4
  3. [3] Anna Gomolińska. On three closely related rough inclusion functions. In Marzena Kryszkiewicz, James F. Peters, Henryk Rybiński, and Andrzej Skowron, editors, Rough Sets and Intelligent Systems Paradigms, volume 4585 of Lecture Notes in Computer Science, pages 142–151, Berlin, Heidelberg, 2007. Springer. doi:10.1007/978-3-540-73451-2_16.10.1007/978-3-540-73451-2_16
  4. [4] Anna Gomolińska. On certain rough inclusion functions. In James F. Peters, Andrzej Skowron, and Henryk Rybiński, editors, Transactions on Rough Sets IX, volume 5390 of Lecture Notes in Computer Science, pages 35–55. Springer Berlin Heidelberg, 2008. doi:10.1007/978-3-540-89876-4_3.10.1007/978-3-540-89876-4_3
  5. [5] Adam Grabowski. On the computer-assisted reasoning about rough sets. In B. Dunin-K¸eplicz, A. Jankowski, A. Skowron, and M. Szczuka, editors, International Workshop on Monitoring, Security, and Rescue Techniques in Multiagent Systems Location, volume 28 of Advances in Soft Computing, pages 215–226, Berlin, Heidelberg, 2005. Springer-Verlag. doi:10.1007/3-540-32370-8_15.10.1007/3-540-32370-8_15
  6. [6] Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371–385, 2014. doi:10.3233/FI-2014-1129.10.3233/FI-2014-1129
  7. [7] Adam Grabowski. Building a framework of rough inclusion functions by means of computerized proof assistant. In Tamás Mihálydeák, Fan Min, Guoyin Wang, Mohua Banerjee, Ivo Düntsch, Zbigniew Suraj, and Davide Ciucci, editors, Rough Sets, volume 11499 of Lecture Notes in Computer Science, pages 225–238, Cham, 2019. Springer International Publishing. ISBN 978-3-030-22815-6. doi:10.1007/978-3-030-22815-6_18.10.1007/978-3-030-22815-6_18
  8. [8] Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.10.3233/FI-2016-1406
  9. [9] Adam Grabowski. Formal development of rough inclusion functions. Formalized Mathematics, 27(4):337–345, 2019. doi:10.2478/forma-2019-0028.10.2478/forma-2019-0028
  10. [10] Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55–64, 2013. doi:10.2478/forma-2013-0006.10.2478/forma-2013-0006
  11. [11] Adam Grabowski. Binary relations-based rough sets – an automated approach. Formalized Mathematics, 24(2):143–155, 2016. doi:10.1515/forma-2016-0011.10.1515/forma-2016-0011
  12. [12] Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.10.1007/978-3-642-14128-7_26
  13. [13] Adam Grabowski and Michał Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183–191, 2018. doi:10.2478/forma-2018-0016.10.2478/forma-2018-0016
  14. [14] Jan Łukasiewicz. Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. In L. Borkowski, editor, Jan Łukasiewicz – Selected Works, pages 16–63. North Holland, Polish Scientific Publ., Amsterdam London Warsaw, 1970. First published in Kraków, 1913.
  15. [15] Zdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.10.1007/BF01001956
  16. [16] Andrzej Skowron and Jarosław Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27(2/3):245–253, 1996. doi:10.3233/FI-1996-272311.10.3233/FI-1996-272311
  17. [17] William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997–5011, 2007.10.1016/j.ins.2007.05.037
DOI: https://doi.org/10.2478/forma-2020-0009 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 105 - 113
Accepted on: Feb 26, 2020
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Published on: May 29, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2020 Adam Grabowski, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.