Have a personal or library account? Click to login
Formalization of Trellises and Tolerance Relations Cover

Formalization of Trellises and Tolerance Relations

Open Access
|Dec 2024

References

  1. Garrett Birkho . Lattice Theory. Providence, Rhode Island, New York, 1967.
  2. Ivan Chajda and Bohdan Zelinka. Weakly associative lattices and tolerance relations. Czechoslovak Mathematical Journal, 26(2):259–269, 1976.
  3. B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.
  4. Ervin Fried and George Grätzer. Some examples of weakly associative lattices. Colloquium Mathematicum, 27:215–221, 1973. doi:10.4064/cm-27-2-215-221.
  5. Adam Grabowski. On fuzzy negations and laws of contraposition. Lattice of fuzzy negations. Formalized Mathematics, 31(1):151–159, 2023. doi:10.2478/forma-2023-0014.
  6. Adam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211–221, 2015. doi:10.1007/s10817-015-9333-5.
  7. Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.
  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:10.1007/978-3-319-66824-6_16.
  9. Adam Grabowski and Takashi Mitsuishi. Formalizing lattice-theoretical aspects of rough and fuzzy sets. In D. Ciucci, G. Wang, S. Mitra, and W.Z. Wu, editors, Rough Sets and Knowledge Technology – 10th International Conference held as part of the International Joint Conference on Rough Sets (IJCRS), Tianjin, PR China, November 20–23, 2015, Proceedings, volume 9436 of Lecture Notes in Artificial Intelligence, pages 347–356. Springer, 2015. doi:10.1007/978-3-319-25754-9 31.
  10. Adam Grabowski and Markus Moschner. Managing heterogeneous theories within a mathematical knowledge repository. In Andrea Asperti, Grzegorz Bancerek, and Andrzej Trybulec, editors, Mathematical Knowledge Management Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 116–129. Springer, 2004. doi:10.1007/978-3-540-27818-4_9. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19–21, 2004.
  11. Adam Grabowski and Christoph Schwarzweller. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49–64. Springer, 2006. doi:10.1007/11618027 4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15–17, 2005, Revised Selected Papers.
  12. Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. Equality in computer proof-assistants. In Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin, editor, Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, volume 5 of ACSIS-Annals of Computer Science and Information Systems, pages 45–54. IEEE, 2015. doi:10.15439/2015F229.
  13. George Grätzer. General Lattice Theory. Academic Press, New York, 1978.
  14. George Grätzer. Lattice Theory: Foundation. Birkhäuser, 2011.
  15. Yu Kong and Bin Zhao. Uninorms on bounded trellises. Fuzzy Sets and Systems, 481: 108898, 2024. doi:10.1016/j.fss.2024.108898.
  16. William McCune and Ranganathan Padmanabhan. Automated Deduction in Equational Logic and Cubic Curves. Springer-Verlag, Berlin, 1996.
  17. Ranganathan Padmanabhan and Sergiu Rudeanu. Axioms for Lattices and Boolean Algebras. World Scientific Publishers, 2008.
  18. Damian Sawicki and Adam Grabowski. On weakly associative lattices and near lattices. Formalized Mathematics, 29(2):77–85, 2021. doi:10.2478/forma-2021-0008.
  19. Helen Skala. Trellis Theory. Providence, R.I.: American Mathematical Society, 1972.
  20. Helen L. Skala. Trellis theory. Algebra Universalis, 1:218–233, 1971. doi:10.1007/BF02944982.
  21. Lemnaouar Zedam and Bernard De Baets. Triangular norms on bounded trellises. Fuzzy Sets and Systems, 462:108468, 2023. doi:10.1016/j.fss.2023.01.003.
DOI: https://doi.org/10.2478/forma-2024-0022 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 271 - 279
Accepted on: Dec 27, 2024
Published on: Dec 31, 2024
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2024 Adam Grabowski, Franciszek Turowski, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.