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  3. Formalized Mathematics
  4. Formalized Mathematics, 2018, Volume 26, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/7638
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    Pole DCWartośćJęzyk
    dc.contributor.authorGrabowski, Adam-
    dc.date.accessioned2019-03-06T12:24:00Z-
    dc.date.available2019-03-06T12:24:00Z-
    dc.date.issued2018-
    dc.identifier.citationFormalized Mathematics, Volume 26, Issue 4, Pages 271-276-
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/7638-
    dc.description.abstractIn the article we continue in the Mizar system [8], [2] the formalization of fuzzy implications according to the monograph of Baczyński and Jayaram “Fuzzy Implications” [1]. We develop a framework of Mizar attributes allowing us for a smooth proving of basic properties of these fuzzy connectives [9]. We also give a set of theorems about the ordering of nine fundamental implications: Łukasiewicz (ILK), Gödel (IGD), Reichenbach (IRC), Kleene-Dienes (IKD), Goguen (IGG), Rescher (IRS), Yager (IYG), Weber (IWB), and Fodor (IFD).This work is a continuation of the development of fuzzy sets in Mizar [6]; it could be used to give a variety of more general operations on fuzzy sets [13]. The formalization follows [10], [5], and [4].-
    dc.language.isoen-
    dc.publisherDeGruyter Open-
    dc.subjectfuzzy implication-
    dc.subjectfuzzy set-
    dc.subjectfuzzy logic-
    dc.titleFundamental Properties of Fuzzy Implications-
    dc.typeArticle-
    dc.identifier.doi10.2478/forma-2018-0023-
    dc.description.AffiliationInstitute of Informatics, University of Białystok, Poland-
    dc.description.referencesMichał Baczyński and Balasubramaniam Jayaram. Fuzzy Implications. Springer Publishing Company, Incorporated, 2008. doi:10.1007/978-3-540-69082-5.-
    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.-
    dc.description.referencesDidier Dubois and Henri Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.-
    dc.description.referencesAdam Grabowski. Formal introduction to fuzzy implications. Formalized Mathematics, 25(3):241–248, 2017. doi:10.1515/forma-2017-0023.-
    dc.description.referencesAdam Grabowski. Basic formal properties of triangular norms and conorms. Formalized Mathematics, 25(2):93–100, 2017. doi:10.1515/forma-2017-0009.-
    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.-
    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.-
    dc.description.referencesAdam 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.-
    dc.description.referencesPetr Hájek. Metamathematics of Fuzzy Logic. Dordrecht: Kluwer, 1998.-
    dc.description.referencesTakashi Mitsuishi, Noboru Endou, and Yasunari Shidama. The concept of fuzzy set and membership function and basic properties of fuzzy set operation. Formalized Mathematics, 9(2):351–356, 2001.-
    dc.description.referencesYasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195–200, 2004.-
    dc.description.referencesPhilippe Smets and Paul Magrez. Implication in fuzzy logic. International Journal of Approximate Reasoning, 1(4):327–347, 1987. doi:10.1016/0888-613X(87)90023-5.-
    dc.description.referencesLotfi Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965. doi:10.1016/S0019-9958(65)90241-X.-
    dc.identifier.eissn1898-9934-
    dc.description.volume26-
    dc.description.issue4-
    dc.description.firstpage271-
    dc.description.lastpage276-
    dc.identifier.citation2Formalized Mathematics-
    dc.identifier.orcid0000-0001-5026-3990-
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2018, Volume 26, Issue 4

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