Intuitionistic Fuzzy Normal Subrings over Normed Rings

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Nour Abed Alhaleem
Abd Ghafur Ahmad


This paper presents the notion of intuitionistic fuzzy normed normal subrings. We investigate the concept of intuitionistic fuzzy normal subrings over normed rings and characterize relevant properties of such subrings. Further, we define direct product of fuzzy normal subrings over normed rings and investigate some related fundamental properties.

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  1. L.A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353.
  2. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517.
  3. W. Wu, Normal fuzzy subgroups, Fuzzy Math. 1 (1981), 21-30.
  4. W. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets Syst. 8 (1982), 133-139.
  5. N. Mukherjee, Fuzzy normal subgroups and fuzzy cosets, Inform. Sci. 34 (1984), 225-239.
  6. W. Wu, Fuzzy congruences and normal fuzzy subgroups, Math. Appl. 1 (1988), 9-20.
  7. M. Mishref, Normal fuzzy subgroups and fuzzy normal series of finite groups, Fuzzy Sets Syst. 72 (1995), 379-383.
  8. S. Abdullah, M. Aslam, T. A. Khan, M. Naeem, A new type of fuzzy normal subgroups and fuzzy cosets, J. Intell. Fuzzy Syst. 25 (2013), 37-47.
  9. K.T. Atanassov, Intuitionistic fuzzy sets, In Intuitionistic Fuzzy Sets, Springer, Berlin, Germany, 1999, 1-137.
  10. K. Hur, S.Y. Jang, H.W. Kang, Intuitionistic fuzzy normal subgroups and intuitionistic fuzzy cosets, Honam Math. J. 26 (2004), 559-587.
  11. M.F. Marashdeh, A.R. Salleh, The intuitionistic fuzzy normal subgroup, Int. J. Fuzzy Log. Intell. Syst. 10 (2010), 82-88.
  12. V. Veeramani, K. Arjunan, N. Palaniappan, Some properties of intuitionistic fuzzy normal subrings, Appl. Math. Sci. 4 (2010), 2119-2124.
  13. P. Sharma, On Intuitionistic fuzzy magnified translation in rings, Int. J. Algebra. 1 (2011), 1451-1458.
  14. N. Abed Alhaleem, A.G. Ahmad, Intuitionistic Fuzzy Normed Subrings and Intuitionistic Fuzzy Normed Ideals, Mathematics. 8 (2020), 1594.
  15. A. Emniyet, M. S ¸ahin, Fuzzy normed rings, Symmetry. 10 (2018), 515.
  16. R. Arens, A generalization of normed rings, Pac. J. Math. 2 (1952), 455-471.
  17. M.A. Najmark, Normed rings, Noordhoff, Groningen, The Netherlands, 1964.
  18. I. Gelfand, D. Raikov, G. Shilov, Commutative Normed Rings, American Mathematical Society, USA, 2002.
  19. A.U Alkouri, A.R. Salleh, Complex Atanassov's intuitionistic fuzzy relation, Abstr. Appl. Anal. 2013 (2013), 287382.
  20. M.O. Alsarahead, A.G. Ahmad, Complex intuitionistic fuzzy ideals, AIP Conf. Proc. 1940 (2018), 020118.
  21. P. Sharma, G. Kaur, On intuitionistic fuzzy prime submodules, Notes IFS. 24 (2018), 97-112.
  22. A. Al-Masarwah, A.G. Ahmad, Structures on Doubt Neutrosophic Ideals of BCK/BCI-Algebras under (s, t)-Norms, Neutrosophic Sets Syst. 33 (2020), 17.
  23. M. Gupta, J. Qi, Theory of t-norms and fuzzy inference methods, Fuzzy Sets Syst. 40 (1991), 431-450.