Submit your research to the International Journal "Notes on Intuitionistic Fuzzy Sets". Contact us at nifs.journal@gmail.com
Call for Papers for the 27th International Conference on Intuitionistic Fuzzy Sets is now open!
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.

Issue:Generalizations of prime intuitionistic fuzzy ideals of a lattice

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/30/1/26-55
Title of paper: Generalizations of prime intuitionistic fuzzy ideals of a lattice
Author(s):
Poonam Kumar Sharma
Post-Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Presented at: Proceedings of the 27th International Conference on Intuitionistic Fuzzy Sets, 5–6 July 2024, Burgas, Bulgaria
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 1, pages 26–55
DOI: https://doi.org/10.7546/nifs.2024.30.1.26-55
Download:  PDF (308  Kb, Info)
Abstract: As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.
Keywords: Lattice, Intuitionistic fuzzy lattice, Intuitionistic fuzzy ideal, Intuitionistic fuzzy prime ideal, Intuitionistic fuzzy 2-absorbing ideal, Intuitionistic fuzzy primary ideal.
AMS Classification: 03F55, 06D72, 03B10.
References:
  1. Ahn, T. C., Hur, K., & Kang, H. W. (2019). Intuitionistic Fuzzy Lattices. International Review of Fuzzy Mathematics, 4(2), 83–100.
  2. Ahn, Y. S., Hur, K., & Kim, D. S. (2005). The lattice of intuitionistic fuzzy ideals of a ring. Journal Of Applied Mathematics And Computing, 19, 551–572.
  3. Amroune, A., & Ziane, B. (2019). More on intuitionistic fuzzy sublattices and their ideals. Facta Universitatis, Series: Mathematics and Informatics, 34(5), 871–888.
  4. Anderson, D. F., & Badawi, A. (2011). On n-absorbing ideals of commutative rings, Communications in Algebra, 39, 1646–1672.
  5. Atanassov, K.T. (1983), Intuitionistic fuzzy sets. In: Sgurev, V. (Ed.). VII ITKR’s session, Deposited in Central Science and Technology Library of the Bulgarian Academy of Sciences, Sofia.
  6. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
  7. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets Theory and Applications, Studies on Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg.
  8. Atanassov, K., & Stoeva, S. (1984). Intuitionistic L-fuzzy sets, Cybernetics and Systems Research, Vol. 2, R. Trappl (ed.) Elsevier Science Publishers B.V., North-Holland, pp. 539–540.
  9. Badawi, A. (2007). On 2-absorbing ideals of commutative rings. Bulletin of the Australian Mathematical Society, 75, 417–429.
  10. Badawi, A., & Darani, A. Y. (2013), On weakly 2-absorbing ideals of commutative rings. Houston Journal of Mathematics, 39(2), 441–452.
  11. Bakhadach, I., Melliani, S., Oukessou, M., & Chadli, S. L. (2016). Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring. Notes on Intuitionistic Fuzzy Sets, 22(2), 59–63.
  12. Basnet, D. K. (2011). Topics in intuitionistic fuzzy algebra. Lambert Academic Publishing.
  13. Boudaoud, S., Zedam, L., & Milles, S. (2020). Principal intuitionistic fuzzy ideals and filters on a lattice. Discussiones Mathematicae General Algebra and Applications, 40, 75–88.
  14. Gerstenkorn, T., & Tepavcevi, A., (2004). Lattice valued intuitionistic fuzzy sets. Central European Journal of Mathematics, 2(3), 388–398.
  15. Gratzer, G., (1978). General Lattice Theory. Academic Press, New York.
  16. Hur, K., Kang, H. W., & Song, H. K. (2004). Intuitionistic fuzzy ideals on a distributive lattice. Proceedings of KIFS Spring Conference, 4(1), 372–377.
  17. Koguep, B. B. N., Nkuimi, C., & Lele, C. (2008). On fuzzy prime ideals of lattice. SAMSA Journal of Pure and Applicable Mathematics, 3, 1–11.
  18. Milles, S., Zedam, L., & Rak, E. (2017). Characterizations of intuitionistic fuzzy ideals and filters based on lattice operations. Journal of Fuzzy Set Valued Analysis, 3, 143–159.
  19. Sharma, P. K. (2022). On intuitionistic fuzzy primary ideal of a ring. Pan-American Journal of Mathematics, 1, 1–11.
  20. Sharma, P. K., Lata, H., & Bharadwaj, N. (2022). A study on intuitionistic fuzzy 2-absorbing primary ideals in Г-ring. Notes on Intuitionistic Fuzzy Sets, 28(3), 280–292.
  21. Thomas, K. V., & Nair, L. S. (2011). Intuitionistic fuzzy sublattices and ideals. Fuzzy Information and Engineering, 3, 321–331.
  22. Wasadikar, M. P., & Gaikwad, K. T., (2015). On 2-absorbing and weakly 2-absorbing ideals of lattices. Mathematical Sciences International Research Journal, 4, 82–85.
  23. Wasadikar, M. P., & Gaikwad, K. T. (2019). Some properties of 2-absorbing primary ideals in lattices. AKCE International Journal of Graphs and Combinatorics, 16, 18–26.
  24. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:Generalizations_of_prime_intuitionistic_fuzzy_ideals_of_a_lattice&oldid=11894"