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Issue:Normality and translation of IFS(G × Q) under norms

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Title of paper: Normality and translation of IFS(G × Q) under norms
Author(s):
Rasul Rasuli
Department of Mathematics, Payame Noor University(PNU), P. O. Box 19395-4697, Tehran, Iran
Rasuli@pnu.ac.ir
Presented at: 26th International Conference on Intuitionistic Fuzzy Sets, Sofia, 26—27 June 2023
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 29 (2023), Number 2, pages 114–132
DOI: https://doi.org/10.7546/nifs.2023.29.2.114-132
Download:  PDF (316  Kb, File info)
Abstract: In this article, we introduce the idea of normality and translation of Q-intuitionistic fuzzy subgroups with respect to norms (t-norm T and t-conorm C) and some interesting results of them are given. Conditions for level cut subsets of them are explored and provided. Finally, we investigate them by using group homomorphisms are investigated.
Keywords: Group theory, Fuzzy set theory, Norms, Intuitionistic fuzzy sets.
AMS Classification: 82D25, 03E72, 47A30.
References:
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  2. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
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  4. Rasuli, R., & Narghi, H. (2019) T-Norms Over Q-Fuzzy Subgroups of Group. Jordan Journal of Mathematics and Statistics, 12(1), 1–13.
  5. Rasuli, R. (2020). Anti Q-fuzzy subgroups under T-conorms. Earthline Journal of Mathematical Science, 4(1), 13–28.
  6. Rasuli, R. (2020). Level subsets and translations of QFST(G). MathLAB Journal, 5(1), 1–11.
  7. Rasuli, R. (2021). Conorms over level subsets and translations of anti Q-fuzzy subgroups. International Journal of Mathematics and Computation, 32(2), 55–67.
  8. Rasuli, R. (2022). Fuzzy d-algebras under t-norms. Engineering and Applied Science Letters, 5(1), 27–36.
  9. Rasuli, R. (2022). t-norms over fuzzy ideals (implicative, positive implicative) of BCK-algebras. Mathematical Analysis and Its Contemporary Applications, 4(2), 17–34.
  10. Rasuli, R. (2022). T-fuzzy subbigroups and normal T-fuzzy subbigroups of bigroups. Journal of Ramanujan Society of Mathematics and Mathematical Sciences, 9(2), 165–184.
  11. Rasuli, R., Hashemi, M. A., & Taherkhani, B. (2022). S-norms and anti fuzzy ideals of BCI-algebras. 10th National Mathematics Conference of the Payame Noor University, Shiraz, May, 2022.
  12. Rasuli, R., Taherkhani, B., & Naraghi, H. (2022). T-fuzzy SU-subalgebras. 10th National Mathematics Conference of the Payame Noor University, Shiraz, May, 2022.
  13. Rasuli, R. (2022). A study of T-fuzzy multigroups and direct product of them. 1th National Conference on Applied Researches in Basic Sciences (Mathematics, Chemistry and Physics), University of Ayatolla Boroujerdi, Iran, May 26–27, 2022.
  14. Rasuli, R. (2022). S-(M,N)-fuzzy subgroups. 1th National Conference on Applied Researches in Basic Sciences (Mathematics, Chemistry and Physics), University of Ayatolla Boroujerdi, Iran, May 26–27, 2022.
  15. Rasuli, R. (2022). Intuitionistic fuzzy BCI-algebras (implicative ideals, closed implicative ideals, commutative ideals) under norms. Mathematical Analysis and its Contemporary Applications, 4(3), 17–34.
  16. Rasuli, R. (2022). Fuzzy vector spaces under norms. Annals of Mathematics and Computer Science, 9, 7–24.
  17. Rasuli, R. (2022). T-fuzzy G-submodules. Scientia Magna, 17(1), 107–118.
  18. Rasuli, R. (2022). Anti fuzzy congruence on product lattices. Proceedings of 7th International Conference on Combinatorics, Cryptography, Computer Science and Computing, Iran University of Science and Technology, Iran, Tehran, November 16–17, 2022.
  19. Rasuli, R. (2022). Anti complex fuzzy Lie subalgebras under S-norms. Mathematical Analysis and Its Contemporary Applications, 4(4), 13–26.
  20. Rasuli, R. (2022). t-conorms over anti fuzzy subgroups on direct product of groups. Annals of Mathematics and Computer Science, 10, 8–18.
  21. Rasuli, R. (2022). T-Fuzzy B-subalgebras and normal T-Fuzzy B-subalgebras of B-algebras. International Journal of Open Problems in Computer Science and Mathematics, 15(4), 57–76.
  22. Rasuli, R. (2023). Norms over intuitionistic fuzzy subgroups on direct product of groups. Communications in Combinatorics, Cryptography & Computer Science, 1, 39–54.
  23. Rasuli, R. (2023). T-norms over complex fuzzy subgroups. Mathematical Analysis and its Contemporary Applications, 5(1), 33–49.
  24. Rasuli, R. (2023). T-fuzzy subalgebras of BCI-algebras. International Journal of Open Problems in Computer Science and Mathematics, 16(1), 55–72.
  25. Rasuli, R. (2023). Norms over Q-intuitionistic fuzzy subgroups of a group. Notes on Intuitionistic Fuzzy Sets, 29(1), 30–45.
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