Fundamental Properties of Fuzzy Implications
References
- [1] Michał Baczyński and Balasubramaniam Jayaram. Fuzzy Implications. Springer Publishing Company, Incorporated, 2008. doi:10.1007/978-3-540-69082-5.10.1007/978-3-540-69082-5
- [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/s10817-017-9440-6.10.1007/s10817-017-9440-6
- [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:10.1515/forma-2017-0023.10.1515/forma-2017-0023
- [5] Adam Grabowski. Basic formal properties of triangular norms and conorms. Formalized Mathematics, 25(2):93–100, 2017. doi:10.1515/forma-2017-0009.10.1515/forma-2017-0009
- [6] 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.
- [7] 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_15.10.1007/978-3-319-19324-3_15
- [8] Adam 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.
- [9] Petr Hájek. Metamathematics of Fuzzy Logic. Dordrecht: Kluwer, 1998.
- [10] 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.
- [11] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195–200, 2004.
- [12] Philippe Smets and Paul Magrez. Implication in fuzzy logic. International Journal of Approximate Reasoning, 1(4):327–347, 1987. doi:10.1016/0888-613X(87)90023-5.10.1016/0888-613X(87)90023-5
- [13] Lotfi Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965. doi:10.1016/S0019-9958(65)90241-X.10.1016/S0019-9958(65)90241-X
Language: English
Page range: 271 - 276
Accepted on: Sep 29, 2018
Published on: Mar 2, 2019
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Related subjects:
© 2019 Adam Grabowski, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.