Essential Implicative UP-Filters and t-Essential Fuzzy Implicative UP-Filters of UP-Algebras

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-123
Published: Nov 13, 2023
Cite as:
Thiti Gaketem, Essential Implicative UP-Filters and t-Essential Fuzzy Implicative UP-Filters of UP-Algebras, Int. J. Anal. Appl., 21 (2023), 123.

Main Article Content

Thiti Gaketem

Abstract

For the purpose of this research, we give the new concept of essential implicative UPfilter from the concept of essential UP-filters in UP-algebras. Although we know that the concept of implicative UP-filters is UP-filters, we have an example showing that the concept of essential UPfilters does not necessarily be essential implicative UP-filters. After that, we extend the concept of essential implicative UP-filters to t-essential fuzzy implicative UP-filters of UP-algebras and study their relationship based on characteristic functions and upper level subsets.

Article Details

References

  1. A. Al-Masarwah, A.G. Ahmad, Novel Concepts of Doubt Bipolar Fuzzy H-Ideals of BCK/BCI-Algebras, Int. J. Innov. Comput. Inf. Control. 14 (2018), 2025–2041. https://doi.org/10.24507/ijicic.14.06.2025.
  2. J. Amjadi, The Essential Ideal Graph of a Commutative Ring, Asian-Eur. J. Math. 11 (2018), 1850058. https://doi.org/10.1142/s1793557118500584.
  3. S. Baupradist, B. Chemat, K. Palanivel, R. Chinram, Essential Ideals and Essential Fuzzy Ideals in Semigroups, J. Discr. Math. Sci. Cryptography. 24 (2020), 223–233. https://doi.org/10.1080/09720529.2020.1816643.
  4. T. Gaketem, R. Chinram, Essential (m, n)-Ideals and Essential Fuzzy (m, n)-Ideals in Semigroups, ICIC Express Lett. 15 (2021), 1037–1044. https://doi.org/10.24507/icicel.15.10.1037.
  5. T. Gaketem, A. Iampan, Essential UP-Ideals and t-Essential Fuzzy UP-Ideals of UP-Algebras, ICIC Express Lett. 15 (2021), 1283–1289. https://doi.org/10.24507/icicel.15.12.1283.
  6. T. Gaketem, P. Khamrot, A. Iampan, Essential UP-Filters and t-Essential Fuzzy UP-Filters of UP-Algebras, ICIC Express Lett. 16 (2022), 1057-1062. https://doi.org/10.24507/icicel.16.10.1057.
  7. T. Gaketem, P. Khamrot, Essential Bipolar Fuzzy Ideals in Semigroups, Int. J. Anal. Appl. 21 (2023), 1. https://doi.org/10.28924/2291-8639-21-2023-1.
  8. P. Khamrot, T. Gaketem, Essential Interval Valued Fuzzy Ideals in Semigroups, ICIC Express Lett. 17 (2023), 989–996. https://doi.org/10.24507/icicel.17.09.989.
  9. Q.P. Hu, X. Li, On BCH-Algebras, Math. Seminar Notes (Kobe Univ.) 11 (1983), 313–320.
  10. 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.
  11. A. Iampan, Introducing Fully UP-Semigroups, Discuss. Math. - Gen. Algebra Appl. 38 (2018), 297–306. https://doi.org/10.7151/dmgaa.1290.
  12. 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.
  13. Y. Imai, 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.
  14. 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.
  15. U. Medhi, K. Rajkhowa, L.K. Barthakur, H.K. Saikia, On Fuzzy Essential Ideals of Rings, Adv. Fuzzy Sets Syst. 5 (2008), 287–299.
  16. U. Medhi, H.K. Saikia, On T-Fuzzy Essential Ideals of Rings, Int. J. Pure Appl. Math. 89 (2013), 343–353. https://doi.org/10.12732/ijpam.v89i3.5.
  17. O.R. Devi, On (∈, ∈ ∨qk )-Fuzzy Essential Ideal of Near-Ring, Int. J. Pure Appl. Math. 86 (2013), 283–292. https://doi.org/10.12732/ijpam.v86i2.4.
  18. K.F. Pawar, R.P. Deore, On Essential Ideal and Radical Class, Int. J. Pure Appl. Math.5 (2012), 1–5.
  19. J.N. Mordeson, D.S. Malik, N. Kuroki, Fuzzy Semigroups, Springer, New York, 2003.
  20. N. Panpetch, T. Muangngao, T. Gaketem, Some Essential Bi-Ideals and Essential Fuzzy Bi-Ideals in a Semigroup, J. Math. Comput. Sci. 28 (2022), 326–334. https://doi.org/10.22436/jmcs.028.04.02.
  21. A. Satirad, P. Mosrijai, A. Iampan, Generalized Power UP-Algebras, Int. J. Math. Comput. Sci. 14 (2019), 17–25.
  22. J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy Sets in UP-Algebras, Ann. Fuzzy Math. Informatics, 12 (2016), 739–756.
  23. C. Prabpayak, U. Leerawat, On Ideals and Congruences in KU-algebras, Sci. Magna. 5 (2009), 54–57.
  24. R. Rittichuai, A. Iampan, R. Chinram, P. Singavananda, Essential Ideals and Their Fuzzifications of Ternary Semigroups, ICIC Express Lett. 17 (2023), 191–199. https://doi.org/10.24507/icicel.17.02.191.
  25. P. Yiarayong, P. Wachirawongsakorn, A New Generalization of BE-Algebras, Heliyon. 4 (2018), e00863. https://doi.org/10.1016/j.heliyon.2018.e00863.
  26. L.A. Zadeh, Fuzzy sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  27. T. Shah, I. Rehman, On LA-Rings of Finitely Nonzero Function, Int. J. Contemp. Math. Sci. 5 (2010), 209–222.