Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

A NOVEL APPROACH TO INTUITIONISTIC FUZZY SETS IN UP-ALGEBRAS

  • Thongngam, Nattaporn (Department of Mathematics and Statistics Faculty of Science, Prince of Songkla University) ;
  • Iampan, Aiyared (Department of Mathematics School of Science, University of Phayao)
  • Received : 2019.08.21
  • Accepted : 2019.09.18
  • Published : 2019.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

The notions of intuitionistic fuzzy UP-subalgebras and intuitionistic fuzzy UP-ideals of UP-algebras were introduced by Kesorn et al. [13]. In this paper, we introduce the notions of intuitionistic fuzzy near UP-filters, intuitionistic fuzzy UP-filters, and intuitionistic fuzzy strong UP-ideals of UP-algebras, prove their generalizations, and investigate their basic properties. Furthermore, we discuss the relations between intuitionistic fuzzy near UP-filters (resp., intuitionistic fuzzy UP-filters, intuitionistic fuzzy strong UP-ideals) and their upper t-(strong) level subsets and lower t-(strong) level subsets in UP-algebras.

Keywords

Acknowledgement

Supported by : University of Phayao

The authors would also like to thank the anonymous referee for giving many helpful suggestion on the revision of present paper.

References

  1. M. A. Ansari, A. Haidar, and A. N. A. Koam, On a graph associated to UP-algebras, Math. Comput. Appl. 23 (4) (2018), 61. https://doi.org/10.3390/mca23040061
  2. M. A. Ansari, A. N. A. Koam, and A. Haider, Rough set theory applied to UP-algebras, Ital. J. Pure Appl. Math. 42 (2019), 388-402.
  3. K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  4. K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst. 61 (1994), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1
  5. M. Bhowmik, T. Senapati, and M. Pal, Intuitionistic L-fuzzy ideals of BG-algebras, Afr. Mat. 25 (2014), 577-590. https://doi.org/10.1007/s13370-013-0139-5
  6. N. Dokkhamdang, A. Kesorn, and A. Iampan, Generalized fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 16 (2) (2018), 171-190. https://doi.org/10.30948/afmi.2018.16.2.171
  7. T. Guntasow, S. Sajak, A. Jomkham, and A. Iampan, Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc. 23 (2) (2017), 1-19. https://doi.org/10.22342/jims.23.2.371.1-19
  8. A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top. 5 (1) (2017), 35-54.
  9. A. Iampan, Introducing fully UP-semigroups, Discuss. Math., Gen. Algebra Appl. 38 (2) (2018), 297-306. https://doi.org/10.7151/dmgaa.1290
  10. A. Iampan, Multipliers and near UP-filters of UP-algebras, Manuscript accepted for publication in J. Discrete Math. Sci. Cryptography, July 2019.
  11. C. Jana, T. Senapati, M. Bhowmik, and M. Pal, On intuitionistic fuzzy G-subalgebras of G-algebras, Fuzzy Inf. Eng. 7 (2) (2015), 195-209. https://doi.org/10.1016/j.fiae.2015.05.005
  12. Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideal of BCK-algebras, Internat. J. Math. & Math. Sci. 24 (12) (2000), 839-849. https://doi.org/10.1155/S0161171200004610
  13. B. Kesorn, K. Maimun, W. Ratbandan, and A. Iampan, Intuitionistic fuzzy sets in UP-algebras, Ital. J. Pure Appl. Math. 34 (2015), 339-364.
  14. K. H. Kim, Intuitionistic (T; S)-normed fuzzy subalgebras of BCK-algebras, J. Chungcheong Math. Soc. 20 (3) (2007), 279-286.
  15. Y. H. Kim and T. E. Jeong, Intuitionistic fuzzy structure of B-algebras, J. Appl. Math. & Computing 2 (1-2) (2006), 491-500.
  16. M. A. Malik and M. Touqeer, Intuitionistic fuzzy BCI-commutative ideals in BCI-algebras, Pakistan J. Sci. 64 (4) (2012), 353-358.
  17. S. M. Mostafa, M. A. A. Naby, and O. R. Elgendy, Intuitionistic fuzzy KU-ideals in KU-algebras, Int. J. Math. Sci. Appl. 1 (3) (2011), 1379-1384.
  18. N. Palaniappan, R. Devi, and P. S. Veerappan, Intuitionistic fuzzy n-fold BCI-positive implicative ideals in BCI-algebras, Int. J. Fuzzy Math. Syst. 3 (1) (2013), 1-11.
  19. C. Prabpayak and U. Leerawat, On ideals and congruences in KU-algebras, Sci. Magna 5 (1) (2009), 54-57.
  20. P. Rangsuk, P. Huana, and A. Iampan, Neutrosophic N-structures over UP-algebras, Neutrosophic Sets Syst. 28 (2019), 87-127.
  21. A. Satirad and A. Iampan, Fuzzy soft sets over fully UP-semigroups, Eur. J. Pure Appl. Math. 12 (2) (2019), 294-331. https://doi.org/10.29020/nybg.ejpam.v12i2.3412
  22. A. Satirad, P. Mosrijai, and A. Iampan, Formulas for nding UP-algebras, Int. J. Math. Comput. Sci. 14 (2) (2019), 403-409.
  23. A. Satirad, P. Mosrijai, and A. Iampan, Generalized power UP-algebras, Int. J. Math. Comput. Sci. 14 (1) (2019), 17-25.
  24. B. Satyanarayana and R. D. Prasad, Some results on intuitionistic fuzzy ideals in BCK-algebras, Gen. Math. Notes 4 (1) (2011), 1-15.
  25. T. Senapati, M. Bhowmik, M. Pal, and B. Davvaz, Atanassov's intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras and ideals in BCK/BCI-algebras, Eurasian Math. J. 6 (1) (2015), 96-114.
  26. T. Senapati and K. P. Shum, Atanassov's interval-valued intuitionistic fuzzy set theory applied in KU-subalgebras, Discrete Math. Algorithms Appl. 11 (2) (2019), 1950023. https://doi.org/10.1142/s179383091950023x
  27. J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform. 12 (6) (2016), 739-756.
  28. M. Songsaeng and A. Iampan, N-fuzzy UP-algebras and its level subsets, J. Algebra Relat. Top. 6 (1) (2018), 1-24.
  29. S. Sun and Q. Li, Intuitionistic fuzzy subalgebras (ideals) with thresholds (${\lambda},{\mu}$) of BCI-algebras, Int. J. Math., Comput., Phys. Quantum Eng. 8 (2) (2014), 436-440.
  30. N. Udten, N. Songseang, and A. Iampan, Translation and density of a bipolar- valued fuzzy set in UP-algebras, Ital. J. Pure Appl. Math. 41 (2019), 469-496.
  31. L. A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  32. J. Zhan and Z. Tan, Intuitionistic fuzzy ${\alpha}$-ideals in BCI-algebras, Soochow J. Math. 30 (2) (2004), 207-216.