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  3. Formalized Mathematics
  4. Formalized Mathematics, 2022, Volume 30, Issue 2

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/14267
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    Pole DCWartośćJęzyk
    dc.contributor.authorMitsuishi, Takashi-
    dc.date.accessioned2022-12-30T11:26:34Z-
    dc.date.available2022-12-30T11:26:34Z-
    dc.date.issued2022-
    dc.identifier.citationFormalized Mathematics, Volume 30, Issue 2, Pages 125-134pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/14267-
    dc.description.abstractIn this study, using the Mizar system [1], [2], we reuse formalization efforts in fuzzy sets described in [5] and [6]. This time the centroid method which is one of the fuzzy inference processes is formulated [10]. It is the most popular of all defuzzied methods ([11], [13], [7]) – here, defuzzified crisp value is obtained from domain of membership function as weighted average [8]. Since the integral is used in centroid method, the integrability and bounded properties of membership functions are also mentioned to fill the formalization gaps present in the Mizar Mathematical Library, as in the case of another fuzzy operators [4]. In this paper, the properties of piecewise linear functions consisting of two straight lines are mainly described.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.subjectdefuzzificationpl
    dc.subjectcentroidpl
    dc.subjectpiecewise linear functionpl
    dc.titleDefinition of Centroid Method as Defuzzificationpl
    dc.typeArticlepl
    dc.rights.holder© 2022 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2022-0010-
    dc.description.AffiliationFaculty of Business and Informatics, Nagano University, Japanpl
    dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.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.referencesNoboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93–102, 1999.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 and Takashi Mitsuishi. Extending Formal Fuzzy Sets with Triangular Norms and Conorms, volume 642: Advances in Intelligent Systems and Computing, pages 176–187. Springer International Publishing, Cham, 2018. doi:10.1007/978-3-319-66824-6_16.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.referencesTetsuro Katafuchi, Kiyoji Asai, and Hiroshi Fujita. Investigation of deffuzification in fuzzy inference: Proposal of a new defuzzification method (in Japanese). Medical Imaging and Information Sciences, 18(1):19–30, 2001. doi:10.11318/mii1984.18.19pl
    dc.description.referencesEbrahim H. Mamdani. Application of fuzzy algorithms for control of simple dynamic plant. IEE Proceedings, 121:1585–1588, 1974.pl
    dc.description.referencesTakashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Basic properties of fuzzy set operation and membership function. Formalized Mathematics, 9(2):357–362, 2001.pl
    dc.description.referencesMasaharu Mizumoto. Improvement of fuzzy control (IV)-case by product-sum-gravity method. In Proc. 6th Fuzzy System Symposium, 1990, pages 9–13, 1990.pl
    dc.description.referencesTimothy J. Ross. Fuzzy Logic with Engineering Applications. John Wiley and Sons Ltd, 2010.pl
    dc.description.referencesYasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195–200, 2004.pl
    dc.description.referencesWerner Van Leekwijck and Etienne E. Kerre. Defuzzification: Criteria and classification. Fuzzy Sets and Systems, 108(2):159–178, 1999.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume30pl
    dc.description.issue2pl
    dc.description.firstpage125pl
    dc.description.lastpage134pl
    dc.identifier.citation2Formalized Mathematicspl
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