Intuitionistic Hesitant Fuzzy UP (BCC)-Filters of UP (BCC)-Algebras

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-27
Published: Mar 17, 2023
Cite as:
Aiyared Iampan, R. Alayakkaniamuthu, P. Gomathi Sundari, N. Rajesh, Intuitionistic Hesitant Fuzzy UP (BCC)-Filters of UP (BCC)-Algebras, Int. J. Anal. Appl., 21 (2023), 27.

Main Article Content

Aiyared Iampan, R. Alayakkaniamuthu, P. Gomathi Sundari, N. Rajesh

Abstract

The concepts of intuitionistic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and UP (BCC)-filters of UP (BCC)-algebras are presented, some of their features are explained, and their extensions are demonstrated using the theory of hesitant fuzzy sets as a foundation. The necessary conditions for those intuitionistic hesitant fuzzy sets are provided and include their relation to their complement. The concept of prime and weakly prime of intuitionistic hesitant fuzzy sets was also introduced and studied. We also talk about the connections between intuitionistic hesitant fuzzy UP (BCC)-subalgebras (UP (BCC)-ideals, UP (BCC)-filters) and their level subsets. The homomorphic pre-images of intuitionistic hesitant fuzzy UP (BCC)-filters in UP (BCC)-algebras are also studied and some related properties are investigated.

Article Details

References

  1. B. Ahmad, A. Kharal, On Fuzzy Soft Sets, Adv. Fuzzy Syst. 2009 (2009), 586507. https://doi.org/10.1155/2009/586507.
  2. M. Atef, M.I. Ali, T.M. Al-shami, Fuzzy Soft Covering-Based Multi-Granulation Fuzzy Rough Sets and Their Applications, Comput. Appl. Math. 40 (2021), 115. https://doi.org/10.1007/s40314-021-01501-x.
  3. I. Beg, T. Rashid, Group Decision Making Using Intuitionistic Hesitant Fuzzy Sets, Int. J. Fuzzy Logic Intell. Syst. 14 (2014), 181–187. https://doi.org/10.5391/ijfis.2014.14.3.181.
  4. N. Caˇgman, S. Enginoˇglu, F. Citak, Fuzzy Soft Set Theory and Its Application, Iran. J. Fuzzy Syst. 8 (2011), 137-147.
  5. T. Guntasow, S. Sajak, A. Jomkham, A. Iampan, Fuzzy Translations of a Fuzzy Set in UP-Algebras, J. Indones. Math. Soc. 23 (2017), 1-19. https://doi.org/10.22342/jims.23.2.371.1-19.
  6. A. Iampan, A New Branch of the Logical Algebra: UP-Algebras, J. Algebra Related Topics. 5 (2017), 35-54. https://doi.org/10.22124/jart.2017.2403.
  7. Y.B. Jun, S.S. Ahn, G. Muhiuddin, Hesitant Fuzzy Soft Subalgebras and Ideals inBCK/BCI-Algebras, Sci. World J. 2014 (2014), 763929. https://doi.org/10.1155/2014/763929.
  8. Y.B. Jun, B. Brundha, N. Rajesh, R.K. Bandaru, (3, 2)-Fuzzy UP (BCC)-Subalgebras and (3, 2)-Fuzzy UP (BCC)- Filters, J. Mahani Math. Res. 11 (2022), 1-14.
  9. Y.B. Jun, S.Z. Song, Hesitant Fuzzy Set Theory Applied to Filters in MTL-Algebras, Honam Math. J. 36 (2014), 813-830. https://doi.org/10.5831/HMJ.2014.36.4.813.
  10. Y. Komori, The Class of BCC-Algebras Is Not a Variety, Math. Japon. 29 (1984), 391-394.
  11. P. Mosrijai, W. Kamti, A. Satirad, A. Iampan, Hesitant Fuzzy Sets on UP-Algebras, Konuralp J. Math. 5 (2017), 268-280.
  12. J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy Sets in UP-Algebras, Ann. Fuzzy Math. Inform. 12 (2016), 739-756.
  13. V. Torra, Hesitant Fuzzy Sets, Int. J. Intell. Syst. 25 (2010), 529-539. https://doi.org/10.1002/int.20418.
  14. V. Torra, Y. Narukawa, On Hesitant Fuzzy Sets and Decision, in: 2009 IEEE International Conference on Fuzzy Systems, IEEE, Jeju Island, South Korea, 2009: pp. 1378–1382. https://doi.org/10.1109/FUZZY.2009.5276884.
  15. L.A. Zadeh, Fuzzy Sets, Inform. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  16. B. Zhu, Z. Xu, M. Xia, Dual Hesitant Fuzzy Sets, J. Appl. Math. 2012 (2012), 879629. https://doi.org/10.1155/2012/879629.