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http://hdl.handle.net/11320/15406
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Pole DC | Wartość | Język |
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dc.contributor.author | Mitsuishi, Takashi | - |
dc.date.accessioned | 2023-10-09T12:19:51Z | - |
dc.date.available | 2023-10-09T12:19:51Z | - |
dc.date.issued | 2023 | - |
dc.identifier.citation | Formalized Mathematics, Volume 31, Issue 1, Pages 59-66 | pl |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.uri | http://hdl.handle.net/11320/15406 | - |
dc.description.abstract | Since isosceles triangular and trapezoidal membership functions [4] are easy to manage, they were applied to various fuzzy approximate reasoning [10], [13], [14]. The centroids of isosceles triangular and trapezoidal membership functions are mentioned in this article [16], [9] and formalized in [11] and [12]. Some propositions of the composition mapping (f +· g, or f +* g using Mizar formalism, where f, g are affine mappings), are proved following [3], [15]. Then different notations for the same isosceles triangular and trapezoidal membership function are formalized. We proved the agreement of the same function expressed with different parameters and formalized those centroids with parameters. In addition, various properties of membership functions on intervals where the endpoints of the domain are fixed and on general intervals are formalized in Mizar [1], [2]. Our formal development contains also some numerical results which can be potentially useful to encode either fuzzy numbers [7], or even fuzzy implications [5], [6] and extends the possibility of building hybrid rough-fuzzy approach in the future [8]. | pl |
dc.language.iso | en | pl |
dc.publisher | DeGruyter Open | pl |
dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
dc.subject | defuzzification | pl |
dc.subject | centroid method | pl |
dc.subject | isosceles triangular function | pl |
dc.subject | isosceles trapezoidal function | pl |
dc.title | Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method | pl |
dc.type | Article | pl |
dc.rights.holder | © 2023 The Author(s) | pl |
dc.rights.holder | CC BY-SA 3.0 license | pl |
dc.identifier.doi | 10.2478/forma-2023-0006 | - |
dc.description.Affiliation | Faculty of Business and Informatics, Nagano University, Japan | pl |
dc.description.references | Grzegorz 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.references | Grzegorz 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 |
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dc.description.references | Eikou Gonda, Hitoshi Miyata, and Masaaki Ohkita. Self-turning of fuzzy rules with different types of MSFs (in Japanese). Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, 16(6):540–550, 2004. doi:10.3156/jsoft.16.540. | pl |
dc.description.references | Adam Grabowski. On fuzzy negations generated by fuzzy implications. Formalized Mathematics, 28(1):121–128, 2020. doi:10.2478/forma-2020-0011. | pl |
dc.description.references | Adam 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.references | Adam 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.references | Adam 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 |
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dc.description.references | Takashi Mitsuishi. Some properties of membership functions composed of triangle functions and piecewise linear functions. Formalized Mathematics, 29(2):103–115, 2021. doi:10.2478/forma-2021-0011. | pl |
dc.description.references | Takashi Mitsuishi. Definition of centroid method as defuzzification. Formalized Mathematics, 30(2):125–134, 2022. doi:10.2478/forma-2022-0010. | pl |
dc.description.references | Masaharu Mizumoto. Improvement of fuzzy control (IV)-case by product-sum-gravity method. In Proc. 6th Fuzzy System Symposium, 1990, pages 9–13, 1990. | pl |
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dc.identifier.eissn | 1898-9934 | - |
dc.description.volume | 31 | pl |
dc.description.issue | 1 | pl |
dc.description.firstpage | 59 | pl |
dc.description.lastpage | 66 | pl |
dc.identifier.citation2 | Formalized Mathematics | pl |
Występuje w kolekcji(ach): | Formalized Mathematics, 2023, Volume 31, Issue 1 |
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