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Definition of Centroid Method as Defuzzification Cover

Definition of Centroid Method as Defuzzification

Open Access
|Dec 2022

References

  1. [1] 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.
  2. [2] 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/s10817-017-9440-6.604425130069070
  3. [3] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93–102, 1999.
  4. [4] 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.
  5. [5] Adam 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.
  6. [6] 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.
  7. [7] Tetsuro Katafuchi, Kiyoji Asai, and Hiroshi Fujita. Investigation of de uzification in fuzzy inference: Proposal of a new defuzzification method (in Japanese). Medical Imaging and Information Sciences, 18(1):19–30, 2001. doi:10.11318/mii1984.18.19.
  8. [8] Ebrahim H. Mamdani. Application of fuzzy algorithms for control of simple dynamic plant. IEE Proceedings, 121:1585–1588, 1974.10.1049/piee.1974.0328
  9. [9] Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Basic properties of fuzzy set operation and membership function. Formalized Mathematics, 9(2):357–362, 2001.
  10. [10] Masaharu Mizumoto. Improvement of fuzzy control (IV)-case by product-sum-gravity method. In Proc. 6th Fuzzy System Symposium, 1990, pages 9–13, 1990.
  11. [11] Timothy J. Ross. Fuzzy Logic with Engineering Applications. John Wiley and Sons Ltd, 2010.
  12. [12] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195–200, 2004.
  13. [13] Werner Van Leekwijck and Etienne E. Kerre. Defuzzification: Criteria and classification. Fuzzy Sets and Systems, 108(2):159–178, 1999.10.1016/S0165-0114(97)00337-0
DOI: https://doi.org/10.2478/forma-2022-0010 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 125 - 134
Accepted on: Jul 23, 2022
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Published on: Dec 24, 2022
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2022 Takashi Mitsuishi, published by University of Białystok
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