Lattice Valued Fuzzy Sets in UP (BCC)-Algebras

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-59
Published: Jun 23, 2023
Cite as:
Aiyared Iampan, Akarachai Satirad, Ronnason Chinram, Rukchart Prasertpong, Pongpun Julatha, Lattice Valued Fuzzy Sets in UP (BCC)-Algebras, Int. J. Anal. Appl., 21 (2023), 59.

Main Article Content

Aiyared Iampan, Akarachai Satirad, Ronnason Chinram, Rukchart Prasertpong, Pongpun Julatha

Abstract

The aim of this paper is to apply the concept of L-fuzzy sets (LFSs) to UP (BCC)-algebras and introduce five types of LFSs in UP (BCC)-algebras: L-fuzzy UP (BCC)-subalgebras, L-fuzzy near UP (BCC)-filters, L-fuzzy UP (BCC)-filters, L-fuzzy UP (BCC)-ideals, and L-fuzzy strong UP (BCC)-ideals. Also, we study the characteristic LFSs, t-level subsets, and the Cartesian product of LFSs in UP (BCC)-algebras.

Article Details

References

  1. S.S. Ahn, J.S. Han, On BP-Algebras, Hacettepe J. Math. Stat. 42 (2013), 551–557.
  2. M. Ansari, A. Haidar, A. Koam, On a Graph Associated to UP-Algebras, Math. Comput. Appl. 23 (2018), 61. https://doi.org/10.3390/mca23040061.
  3. M.A. Ansari, A.N.A. Koam, A. Haider, Rough Set Theory Applied to UP-Algebras, Italian J. Pure Appl. Math. 42 (2019), 388–402.
  4. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/s0165-0114(86)80034-3.
  5. M. Chandramouleeswaran, P. Muralikrishna, On Intuitionistic L-Fuzzy Subalgebras of BG-Algebras, Int. Math. Forum, 5 (2010), 995–1000.
  6. B.A. Davey, H.A. Priestley, Introduction to Lattices and Order, Cambridge University, Cambridge, (2002).
  7. N. Dokkhamdang, A. Kesorn, A. Iampan, Generalized Fuzzy Sets in UP-Algebras, Ann. Fuzzy Math. Inform. 16 (2018), 171–190. https://doi.org/10.30948/afmi.2018.16.2.171.
  8. J.A. Goguen, L-Fuzzy Sets, J. Math. Anal. Appl. 18 (1967), 145–174.
  9. 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.
  10. Y. Huang, BCI-Algebra, Science Press, Beijing, (2006).
  11. 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.
  12. A. Iampan, Introducing Fully UP-Semigroups, Discuss. Math. - Gen. Algebra Appl. 38 (2018), 297–306. https://doi.org/10.7151/dmgaa.1290.
  13. A. Iampan, Multipliers and Near UP-Filters of UP-Algebras, J. Discr. Math. Sci. Cryptography. 24 (2019), 667-680. https://doi.org/10.1080/09720529.2019.1649027.
  14. A. Iampan, A. Satirad, M. Songsaeng, A Note on UP-Hyperalgebras, J. Algebraic Hyperstruct. Log. Algebras. 1 (2020), 77–95. https://doi.org/10.29252/hatef.jahla.1.2.7.
  15. A. Iampan, M. Songsaeng, G. Muhiuddin, Fuzzy Duplex UP-Algebras, Eur. J. Pure Appl. Math. 13 (2020), 459–471. https://doi.org/10.29020/nybg.ejpam.v13i3.3752.
  16. Y. Imai and K. Iséki, On axiom systems of propositional calculi, XIV, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 19–22. https://doi.org/10.3792/pja/1195522169.
  17. K. Iséki, An Algebra Related With a Propositional Calculus, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 26–29. https://doi.org/10.3792/pja/1195522171.
  18. Y.C. Jefferson, M. Chandramouleeswaran, On Intuitionistic L-Fuzzy Ideals of BP-Algebras, Int. J. Pure. Appl. Math. 112 (2017), 113–122.
  19. 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. https://doi.org/10.22103/jmmrc.2022.18786.1191.
  20. Y.B. Jun, A. Iampan, Comparative and Allied UP-Filters, Lobachevskii J. Math. 40 (2019), 60–66. https://doi.org/10.1134/s1995080219010086.
  21. Y.B. Jun, A. Iampan, Implicative UP-Filters, Afr. Mat. 30 (2019), 1093–1101. https://doi.org/10.1007/s13370-019-00704-0.
  22. Y.B. Jun, A. Iampan, Shift Up-Filters and Decompositions of Up-Filters in Up-Algebras, Missouri J. Math. Sci. 31 (2019), 36–45. https://doi.org/10.35834/mjms/1559181624.
  23. Y.B. Jun, M.A. Öztürk, G. Muhiuddin, A Generalization of (∈, ∈ ∨q)-Fuzzy Subgroups, Int. J. Math. Stat. 5 (2016), 7–18. https://doi.org/10.20454/ijas.2016.1041.
  24. C.B. Kim, H.S. Kim, On BG-Algebras, Demonstr. Math. 41 (2008), 497–505. https://doi.org/10.1515/dema-2008-0303.
  25. Y. Komori, The Class of BCC-Algebras Is Not a Variety, Math. Japon. 29 (1984), 391–394. https://cir.nii.ac.jp/crid/1573668924920916224.
  26. K.M. Lee, Bipolar-Valued Fuzzy Sets and Their Operations, in: Proc. Int. Conf. On Intelligent Technologies, Bangkok, Thailand, (2000), 307–312. https://cir.nii.ac.jp/crid/1573387450677828352.
  27. J. Neggers, H.S. Kim, On β-Algebras, Mat. Vesnik, 54 (2002), 21–29.
  28. P. Poungsumpao, W. Kaijae, S. Arayarangsi, A. Iampan, Fuzzy UP-Ideals and Fuzzy UP-Subalgebras of UP-Algebras in Term of Level Subsets, Int. J. Math. Comput. Sci. 14 (2019), 647–674.
  29. C. Prabpayak, U. Leerawat, On Ideals and Congruences in KU-Algebras, Sci. Magna, 5 (2009), 54–57.
  30. K. Rajam, M. Chandramouleeswaran, L-Fuzzy β-Subalgebras of β-Algebras, Appl. Math. Sci. 8 (2014), 4241–4248. https://doi.org/10.12988/ams.2014.45322.
  31. A. Satirad, R. Chinram, A. Iampan, Four New Concepts of Extensions of KU/UP-Algebras, Missouri J. Math. Sci. 32 (2020), 138–157. https://doi.org/10.35834/2020/3202138.
  32. A. Iampan, A. Satirad, Topological UP-Algebras, Discuss. Math. - Gen. Algebra Appl. 39 (2019), 231–250. https://doi.org/10.7151/dmgaa.1317.
  33. A. Satirad, P. Mosrijai, A. Iampan, Formulas for Finding UP-Algebras, Int. J. Math. Comput. Sci. 14 (2019), 403–409.
  34. A. Satirad, P. Mosrijai, A. Iampan, Generalized Power UP-Algebras, Int. J. Math. Comput. Sci. 14 (2019), 17–25.
  35. T. Senapati, Y.B. Jun, K.P. Shum, Cubic Set Structure Applied in UP-Algebras, Discrete Math. Algorithm. Appl. 10 (2018), 1850049. https://doi.org/10.1142/s1793830918500490.
  36. T. Senapati, G. Muhiuddin, K.P. Shum, Representation of UP-Algebras in Interval-Valued Intuitionistic Fuzzy Environment, Italian J. Pure Appl. Math. 38 (2017), 497–517.
  37. J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy Sets in UP-Algebras, Ann. Fuzzy Math. Inform. 12 (2016), 739–756.
  38. S. Subramanian, R. Nagarajan, A. Mohan, Cartesian Product of Bi Polar Q-Fuzzy Lattice, Appl. Math. Sci. 6 (2012), 957–968.
  39. L.A. Zadeh, Fuzzy Sets, Inform. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.