Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

AN IMPLICATIVE FILTER OF BE-ALGEBRAS IN CONNECTION WITH CUBIC INTUITIONISTIC FUZZY SETS

  • Rajab Ali, Borzooei (Department of Mathematics, Shahid Beheshti University) ;
  • Hee Sik, Kim (Department of Mathematics, Hanyang University) ;
  • Young Bae, Jun (Department of Mathematics Education, Gyeongsang Naional University) ;
  • Sun Shin, Ahn (Department of Mathematics Education, Dongguk University)
  • Received : 2022.04.18
  • Accepted : 2022.08.23
  • Published : 2022.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

The notions of cubic intuitionistic fuzzy set to filters and implicative filters of BE-algebras are introduced. Relations between cubic intuitionistic fuzzy filters with cubic intuitionistic fuzzy implicative filters of BE-algebras are investigated. The homomorphic image and inverse image of cubic intuitionistic fuzzy filters are studied and some related properties are investigated. Also, the product of cubic intuitionistic fuzzy subalgebras (implicative filters) of BE-algebras are investigated.

Keywords

Acknowledgement

The authors wish to thank the anonymous reviewers for their valuable suggestions.

References

  1. S. S. Ahn and K. K. So, On ideals and upper sets in BE-algebras, Sci. Math. Japon. 68 (2008), 279-285.
  2. S. S. Ahn and K. K. So, On genrealized upper sets in BE-algebras, Bull. Korean Math. Soc. 46 (2009), 281-287. https://doi.org/10.4134/BKMS.2009.46.2.281
  3. K. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31 (1989), no. 3, 343-349. https://doi.org/10.1016/0165-0114(89)90205-4
  4. M. Gulistan, N. Yaqoob, T. Vougiouklis, and H. Abdul Wahab, Extensions of cubic ideals in weak left almost semihypergroups, J. Intell. Fuzzy Syst. 34 (2018), no. 6, 4161-4172. https://doi.org/10.3233/JIFS-171744
  5. M. Gulistan and A. M. Al-roqi, Cubic soft sets with applications in BCK/BCIalgebras, Ann. Fuzzy Math. Inf. 8 (2014), 291-304.
  6. Y. B. Jun and S. S. Ahn, Fuzzy implicative filters with degree in the interval (0, 1], J. Comput. Anal. Appl. 15 (2013), 1456-1466.
  7. Y. B. Jun, C. S. Kim, and K. O. Yang, Cubic sets, Ann. Fuzzy Math. Inf. 4 (2012), 83-98.
  8. Y. B. Jun, G. Muhiuddin, M. A. Ozturk, and E. H. Roh, Cubic soft ideals in BCK/BCI-algebras, J. Comput. Anal. Appl. 22 (2017), 929-940.
  9. Y. B. Jun, A novel extension of cubic sets and its applications in BCK/BCIalgebras, Ann. Fuzzy Math. Inf. 14 (2017), no. 5, 475-486. https://doi.org/10.30948/afmi.2017.14.5.475
  10. M. Khan, Y. B. Jun, M. Gulistan, and N. Yaqoob, The generalized version of Jun's cubic sets in semigroups, J. Intell. Fuzzy Syst. 28 (2015), no. 2, 947-960. https://doi.org/10.3233/IFS-141377
  11. H. S. Kim and Y. H. Kim, On BE-algebras, Sci. Math. Japon. 66 (2007), 113-116.
  12. G. Muhiuddin, F. Feng, and Y. B. Jun, Subalgebras of BCK/BCI-algebras based on cubic soft sets, Sci. World J. 2014 (2014), no. 9, Aricle ID 458638.
  13. T. Senapati, C. S. Kim, M. Bhowmik, and M. Pal, Cubic subalgebras and cubic closed ideals of B-algebras, Fuzzy Inf. Eng. 7 (2015), no. 2, 129-149. https://doi.org/10.1016/j.fiae.2015.05.001
  14. T. Senapati and K. P. Shum, Cubic implicative ideals of BCK-algebras, Missouri J. Math. Sci. 29 (2017), no. 2, 125-138.
  15. T. Senapati, Y. B. Jun, G. Muhiuddin, and K. P. Shum, Cubic intuitionistic structures applied to ideals of BCI-algebras, An. St. Univ. Ovidius Constanta 25 (2019), no. 2, 213-232.
  16. T. Senapati, Y. B. Jun, and K. P. Shum, Cubic intuitionistic subalgebras and closed cubic intuitionistic ideals of B-algebras, J. Intell. Fuzzy Syst. 36 (2019), no. 2, 1563-1571.  https://doi.org/10.3233/JIFS-18518