On Fuzzy Negations Generated by Fuzzy Implications
References
- [1] Michał Baczyński and Balasubramaniam Jayaram. Fuzzy Implications. Springer Publishing Company, Incorporated, 2008. doi:<a href="https://doi.org/10.1007/978-3-540-69082-5.10.1007/978-3-540-69082-5" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/978-3-540-69082-5.10.1007/978-3-540-69082-5</a>
- [2] 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:<a href="https://doi.org/10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17</a>
- [3] Didier Dubois and Henri Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.
- [4] Adam Grabowski. Formal introduction to fuzzy implications. Formalized Mathematics, 25(3):241–248, 2017. doi:<a href="https://doi.org/10.1515/forma-2017-0023.10.1515/forma-2017-0023" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1515/forma-2017-0023.10.1515/forma-2017-0023</a>
- [5] Adam Grabowski. Fundamental properties of fuzzy implications. Formalized Mathematics, 26(4):271–276, 2018. doi:<a href="https://doi.org/10.2478/forma-2018-0023.10.2478/forma-2018-0023" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.2478/forma-2018-0023.10.2478/forma-2018-0023</a>
- [6] Adam Grabowski. Basic formal properties of triangular norms and conorms. Formalized Mathematics, 25(2):93–100, 2017. doi:<a href="https://doi.org/10.1515/forma-2017-0009.10.1515/forma-2017-0009" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1515/forma-2017-0009.10.1515/forma-2017-0009</a>
- [7] 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.
- [8] 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:<a href="https://doi.org/10.1007/978-3-319-66824-6_16.10.1007/978-3-319-66824-6_16" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/978-3-319-66824-6_16.10.1007/978-3-319-66824-6_16</a>
- [9] 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:<a href="https://doi.org/10.1007/978-3-319-19324-3_15.10.1007/978-3-319-19324-3_15" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/978-3-319-19324-3_15.10.1007/978-3-319-19324-3_15</a>
- [10] Petr Hájek. Metamathematics of Fuzzy Logic. Dordrecht: Kluwer, 1998.<a href="https://doi.org/10.1007/978-94-011-5300-3" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/978-94-011-5300-3</a>
- [11] Takashi 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.
- [12] Lotfi Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965. doi:<a href="https://doi.org/10.1016/S0019-9958(65)90241-X.10.1016/S0019-9958(65)90241-X" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/S0019-9958(65)90241-X.10.1016/S0019-9958(65)90241-X</a>
Language: English
Page range: 121 - 128
Accepted on: Feb 26, 2020
Published on: May 29, 2020
Published by: University of Bialystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 times per year
Keywords:
Related subjects:
© 2020 Adam Grabowski, published by University of Bialystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.