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  4. Formalized Mathematics, 2023, Volume 31, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/15852
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    Pole DCWartośćJęzyk
    dc.contributor.authorGrabowski, Adam-
    dc.date.accessioned2024-01-25T09:21:18Z-
    dc.date.available2024-01-25T09:21:18Z-
    dc.date.issued2023-
    dc.identifier.citationFormalized Mathematics, Volume 31, Issue 1, Pages 151-159pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/15852-
    dc.description.abstractThis the next article in the series formalizing the book of Baczyński and Jayaram “Fuzzy Implications”. We define the laws of contraposition connected with various fuzzy negations, and in order to make the cluster registration mechanism fully working, we construct some more non-classical examples of fuzzy implications. Finally, as the testbed of the reuse of lattice-theoretical approach, we introduce the lattice of fuzzy negations and show its basic properties.pl
    dc.language.isoenpl
    dc.publisherDeGruyter Openpl
    dc.rightsAttribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)pl
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/3.0/pl
    dc.subjectfuzzy implicationpl
    dc.subjectcontrapositive symmetrypl
    dc.subjectfuzzy negationpl
    dc.titleOn Fuzzy Negations and Laws of Contraposition. Lattice of Fuzzy Negationspl
    dc.typeArticlepl
    dc.rights.holder© 2022 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2023-0014-
    dc.description.AffiliationFaculty of Computer Science, University of Białystok, Polandpl
    dc.description.referencesMichał Baczyński and Balasubramaniam Jayaram. Fuzzy Implications. Springer Publishing Company, Incorporated, 2008. doi:10.1007/978-3-540-69082-5.pl
    dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.pl
    dc.description.referencesJózef Drewniak. Invariant fuzzy implications. Soft Computing, 10:506–513, 2006.pl
    dc.description.referencesDidier Dubois and Henri Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.pl
    dc.description.referencesAdam Grabowski. Formal introduction to fuzzy implications. Formalized Mathematics, 25(3):241–248, 2017. doi:10.1515/forma-2017-0023.pl
    dc.description.referencesAdam Grabowski. On fuzzy negations generated by fuzzy implications. Formalized Mathematics, 28(1):121–128, 2020. doi:10.2478/forma-2020-0011.pl
    dc.description.referencesAdam Grabowski. Fuzzy implications in the Mizar system. In 30th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2021, Luxembourg, July 11–14, 2021, pages 1–6. IEEE, 2021. doi:10.1109/FUZZ45933.2021.9494593.pl
    dc.description.referencesAdam Grabowski. On the computer certification of fuzzy numbers. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, 2013 Federated Conference on Computer Science and Information Systems (FedCSIS), Federated Conference on Computer Science and Information Systems, pages 51–54, 2013.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 and Takashi Mitsuishi. Initial comparison of formal approaches to fuzzy and rough sets. In Leszek Rutkowski, Marcin Korytkowski, Rafal Scherer, Ryszard Tadeusiewicz, Lotfi A. Zadeh, and Jacek M. Zurada, editors, Artificial Intelligence and Soft Computing – 14th International Conference, ICAISC 2015, Zakopane, Poland, June 14-18, 2015, Proceedings, Part I, volume 9119 of Lecture Notes in Computer Science, pages 160–171. Springer, 2015. doi:10.1007/978-3-319-19324-3_15.pl
    dc.description.referencesAdam Grabowski and Takashi Mitsuishi. Formalizing lattice-theoretical aspects of rough and fuzzy sets. In D. Ciucci, G. Wang, S. Mitra, and W.Z. Wu, editors, Rough Sets and Knowledge Technology – 10th International Conference held as part of the International Joint Conference on Rough Sets (IJCRS), Tianjin, PR China, November 20–23, 2015, Proceedings, volume 9436 of Lecture Notes in Artificial Intelligence, pages 347–356. Springer, 2015. doi:10.1007/978-3-319-25754-9_31.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.referencesTakashi Mitsuishi. Definition of centroid method as defuzzification. Formalized Mathematics, 30(2):125–134, 2022. doi:10.2478/forma-2022-0010.pl
    dc.description.referencesTakashi Mitsuishi. Isosceles triangular and isosceles trapezoidal membership functions using centroid method. Formalized Mathematics, 31:59–66, 2023. doi:10.2478/forma-2023-0006.pl
    dc.description.referencesLotfi Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965. doi:10.1016/S0019-9958(65)90241-X.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume31pl
    dc.description.issue1pl
    dc.description.firstpage151pl
    dc.description.lastpage159pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0001-5026-3990-
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2023, Volume 31, Issue 1

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