As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: September/October 2024.
Open Call for Papers: International Workshop on Intuitionistic Fuzzy Sets • 13 December 2024 • Banska Bystrica, Slovakia/ online (hybrid mode).
Deadline for submissions: 16 November 2024.

Issue:Z2-graded intuitionistic L-fuzzy q-deformed quantum subspaces of Aq

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/28/2/93-112
Title of paper: Z2-graded intuitionistic L-fuzzy q-deformed quantum subspaces of Aq
Author(s):
Marzieh Mostafavi
Department of Mathematics, University of Qom, Qom, Iran
mmostafavi14279@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 2, pages 93–112
DOI: https://doi.org/10.7546/nifs.2022.28.2.93-112
Download:  PDF (247  Kb, File info)
Abstract: In this paper, assuming that ⟨L, ≤〉 is a lattice set with a few specific conditions, intuitionistic L-fuzzy subalgebras, intuitionistic L-fuzzy subcoalgebras and intuitionistic L-fuzzy left (right) coideals are defined and the properties of intuitionistic L-fuzzy subcoalgebras under homomorphisms of coalgebras are investigated. Duality of intuitionistic L-fuzzy subalgebras and duality of intuitionistic L-fuzzy subcoalgebras are also discussed. Intuitionistic L-fuzzy subbialgebras as well as intuitionistic L-fuzzy Hoph subalgebras are studied. Intuitionistic L-fuzzy quantum subsets of kq[x, y] are established and also Z2-graded intuitionistic L-fuzzy q-deformed quantum subspaces of Aq are introduced.
Keywords: Intuitionistic L-fuzzy subcoalgebras, Intuitionistic L-fuzzy Hoph subalgebras, Z2-graded intuitionistic L-fuzzy q-deformed quantum subspaces.
AMS Classification: 08A72, 16T05, 17B05.
References:
  1. Abe, E. (1980). Hoph Algebras. Cambridge Tracts in Mathematics. Cambridge University Press.
  2. Akram, M. (2008). Intuitionistic fuzzy Lie ideals of Lie algebras. International Journal of Fuzzy Mathematics, 16(4), 991–1008.
  3. Atanassov, K. (1983). Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal Bioautomation, 2016, 20(S1), S1–S6. (in English).
  4. Atanassov, K. T. & Stoeva, S. (1983) Intuitionistic fuzzy sets, Polish Symposium on Interval & Fuzzy Mathematics, Poznan, Aug. Proc. 23-26.
  5. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
  6. Atanassov, K. T. (1994). New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems, 61, 137–142.
  7. Atanassov, K. T. (2012). Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag, Berlin.
  8. Atanassov, K. T., & Stoeva, S. (1984). Intuitionistic L-fuzzy sets. In: Trappl, R. (Ed.), Cybernetics and Systems Research 2, Elsevier Sci. Publ., Amsterdam), 539–540.
  9. Banerjee, B., & Basnet, D. (2003). Intuitionistic fuzzy subrings and ideals. Journal of Fuzzy Mathematics, 11(1), 139–155.
  10. Biswas, R. (1989). Intuitionistic fuzzy subgroups. Mathematical Forum, 10, 37–46.
  11. Brown, K., & Goodearl, K. R. (2002). Lectures on Algebraic Quantum Groups. Birkhauser.
  12. Chen, W. (2009). Fuzzy subcoalgebras and duality. Bulletin of the Malaysian Mathematical Sciences Society (2), 32(3), 283–294.
  13. Dascalescu, S., Nastasescu, C., & Raianu, S. (2001). Hopf Algebras, Dekker, New York.
  14. Davvaz, B., Dudek, W. A., & Jun, Y. B. (2006). Intuitionistic fuzzy Hν-submodules. Information Sciences, 176, 285–300.
  15. Drinfeld, V. G. (1986). Quantum groups. Proceedings International Congress of Mathematicians, Berkeley, 798–820.
  16. Dvurecenskij, A., & Chovanec, F. (1988). Fuzzy quantum spaces and compatibility. International Journal of Theoretical Physics, 27(9), 1069–1082.
  17. El-Badawy Yehia, S. (1996). Fuzzy ideals and fuzzy subalgebras of Lie algebras. Fuzzy Sets and Systems, 80, 237–244.
  18. Faddeev, L. D., Reshetikhin, N. Y., & Takhtajan, L. A. (1989). Quantization of Lie groups and Lie algebras, Algebra i Analiz, 1(1), 178–206.
  19. Gargov, G., & Atanassov, K. T. (1992). Two results in intuitionistic fuzzy logic. Comptes rendus de l’Academie bulgare des Sciences, 45(12), 29–31.
  20. Gargov, G., & Atanassov, K. T. (1995). On the intuitionistic fuzzy logic operations. Notes on Intuitionistic Fuzzy Sets, 1(1), 1–4.
  21. Gargov, G., & Atanassov, K. T. (1996). An intuitionistic fuzzy interpretation of the basic axiom of the resolution. Notes on Intuitionistic Fuzzy Sets, 2(3), 20–21.
  22. Hur, K., Jang, S. Y., & Kang, H. W. (2005). Intuitionistic fuzzy ideals of a ring. Journal of the Korean Society of Mathematical Education Series B-pure and Applied Mathematics, 12(3), 193–209.
  23. Hur, K., Kang, H. W., & Song, H. K. (2003). Intuitionistic fuzzy subgroups and subrings. Honam Mathematical Journal, 25(1), 19–41.
  24. Kruszynski, P., & Woronowicz, S. L. (1982). A noncommutative Gelfand–Naimark theorem. Journal of Operator Theory, 8, 361–389.
  25. Manin, Y. I. (1988). Quantum Groups and Non-Commutative Geometry. Centre de Recherches Mathematiques, Universit ´ e de Montr ´ eal. ´
  26. Manin, Y. I. (1989). Multiparametric quantum deformation of the general linear supergroup. Communications in Mathematical Physics, 123, 163–175.
  27. Mostafavi, M. (2020). C∞ L-Fuzzy manifolds with gradation of openness and C∞ LG-fuzzy mappings of them. Iranian Journal of Fuzzy Systems, 17(6), 157–174.
  28. Mostafavi, M. (2022). Quantum Partial Derivatives of Q-analytic Functions On Quantum Superspace Aq. International Journal of Open Problems in Computer Science and Mathematics, 15(1), 81–93.
  29. Navara, M. (1994). Algebraic approach to fuzzy quantum spaces. Demonstratio Mathematica, XXVII (3–4), 589–600.
  30. Pykacz, J. (2007). Quantum structures and fuzzy set theory. In: Engesser, K., Gabbay, D. M., & Lehmann, D. (Eds.), Handbook of Quantum Logic and Quantum Structures, 55–74.
  31. Vaksman, L. L., & Soibelman, J. S. (1988). Algebra of functions on quantum group SU(2). Functional Analysis and Its Applications, 22(3), 170–181.
  32. Vallin, J. M. (1985). C∗-algebres de Hopf et C∗-algebres de Kac. Proceedings of the London Mathematical Society, 50(3), 131–174.
  33. Wachter, H. (2007). Analysis on q-deformed quantum spaces. International Journal of Modern Physics A, 22(1), 95–164.
  34. Woronowicz, S. L. (1987). Compact matrix pseudogroups. Communications in Mathematical Physics, 111(4), 613–665.
  35. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 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:Z2-graded_intuitionistic_L-fuzzy_q-deformed_quantum_subspaces_of_Aq&oldid=11218"