Formal Development of Rough Inclusion Functions

[1] Anna Gomolińska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103–119, 2002.Search in Google Scholar

[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_4Search in Google Scholar

[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_16Search in Google Scholar

[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_3Search in Google Scholar

[5] Adam Grabowski. On the computer-assisted reasoning about rough sets. In B. Dunin-Kęplicz, 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_15Search in Google Scholar

[6] Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371–385, 2014. doi:10.3233/FI-2014-1129.10.3233/FI-2014-1129Search in Google Scholar

[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_18Search in Google Scholar

[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-2016-1406Search in Google Scholar

[9] Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55–64, 2013. doi:10.2478/forma-2013-0006.10.2478/forma-2013-0006Search in Google Scholar

[10] 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-2016-0011Search in Google Scholar

[11] 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_26Search in Google Scholar

[12] 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-2018-0016Search in Google Scholar

[13] Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.10.1007/s10817-015-9345-1Search in Google Scholar

[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.Search in Google Scholar

[15] Zdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.10.1007/BF01001956Search in Google Scholar

[16] Lech Polkowski. Rough mereology. In Approximate Reasoning by Parts, volume 20 of Intelligent Systems Reference Library, pages 229–257, Berlin, Heidelberg, 2011. Springer. ISBN 978-3-642-22279-5. doi:10.1007/978-3-642-22279-5_6.10.1007/978-3-642-22279-5_6Search in Google Scholar

[17] Lech Polkowski and Andrzej Skowron. Rough mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning, 15(4):333–365, 1996. doi:10.1016/S0888-613X(96)00072-2.10.1016/S0888-613X(96)00072-2Search in Google Scholar

[18] 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-1996-272311Search in Google Scholar

[19] William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997–5011, 2007.10.1016/j.ins.2007.05.037Search in Google Scholar