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  3. Formalized Mathematics
  4. Formalized Mathematics, 2020, Volume 28, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/9227
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    Pole DCWartośćJęzyk
    dc.contributor.authorGrabowski, Adam-
    dc.date.accessioned2020-06-16T07:23:59Z-
    dc.date.available2020-06-16T07:23:59Z-
    dc.date.issued2020-
    dc.identifier.citationFormalized Mathematics, Volume 28, Issue 1, Pages 105-113pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/9227-
    dc.description.abstractWe continue the formal development of rough inclusion functions (RIFs), continuing the research on the formalization of rough sets [15] – a well-known tool of modelling of incomplete or partially unknown information. In this article we give the formal characterization of complementary RIFs, following a paper by Gomolinska [4].We expand this framework introducing Jaccard index, Steinhaus generate metric, and Marczewski-Steinhaus metric space [1]. This is the continuation of [9]; additionally we implement also parts of [2], [3], and the details of this work can be found in [7].pl
    dc.language.isoenpl
    dc.publisherDeGruyter Openpl
    dc.rightsUznanie autorstwa-Na tych samych warunkach 3.0 Polska*
    dc.rights.urihttp://creativecommons.org/licenses/by-sa/3.0/pl/*
    dc.subjectrough setpl
    dc.subjectrough inclusion functionpl
    dc.subjectSteinhaus generate metricpl
    dc.titleDeveloping Complementary Rough Inclusion Functionspl
    dc.typeArticlepl
    dc.identifier.doi10.2478/forma-2020-0009-
    dc.description.AffiliationInstitute of Informatics, University of Białystok, Polandpl
    dc.description.referencesMichel Marie Deza and Elena Deza. Encyclopedia of distances. Springer, 2009. doi:10.1007/978-3-642-30958-8.pl
    dc.description.referencesAnna Gomolinska. 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.pl
    dc.description.referencesAnna Gomolinska. On three closely related rough inclusion functions. In Marzena Kryszkiewicz, James F. Peters, Henryk Rybinski, 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.pl
    dc.description.referencesAnna Gomolinska. On certain rough inclusion functions. In James F. Peters, Andrzej Skowron, and Henryk Rybinski, 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.pl
    dc.description.referencesAdam 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.pl
    dc.description.referencesAdam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371–385, 2014. doi:10.3233/FI-2014-1129.pl
    dc.description.referencesAdam 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.pl
    dc.description.referencesAdam 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.pl
    dc.description.referencesAdam Grabowski. Formal development of rough inclusion functions. Formalized Mathematics, 27(4):337–345, 2019. doi:10.2478/forma-2019-0028.pl
    dc.description.referencesAdam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55–64, 2013. doi:10.2478/forma-2013-0006.pl
    dc.description.referencesAdam Grabowski. Binary relations-based rough sets – an automated approach. Formalized Mathematics, 24(2):143–155, 2016. doi:10.1515/forma-2016-0011.pl
    dc.description.referencesAdam 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.pl
    dc.description.referencesAdam Grabowski and Michał Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183–191, 2018. doi:10.2478/forma-2018-0016.pl
    dc.description.referencesJan 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.pl
    dc.description.referencesZdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.pl
    dc.description.referencesAndrzej Skowron and Jarosław Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27(2/3):245–253, 1996. doi:10.3233/FI-1996-272311.pl
    dc.description.referencesWilliam Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997–5011, 2007.pl
    dc.identifier.eissn1898-9934-
    dc.description.firstpage105pl
    dc.description.lastpage113pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0001-5026-3990-
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2020, Volume 28, Issue 1

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