International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

A Proposed Method for Establishing Five Algebraic Substructures in UP-Algebras in View of Generalized Neutrosophic Structures

  • Mohammed Alqahtani*
  • Majdoleen Abuqamar
  • Anas Al-Masarwah

    * Corresponding author

    Abstract

    The main goal of this paper is to utilize the notion of generalized neutrosophic structures (GNSs) to five types of algebraic substructures in UP-algebras. We present the concepts of generalized neutrosophic UP-subalgebras (GNUP-Ss), generalized neutrosophic near UP-filters (GNNUP-Fs), generalized neutrosophic UP-filters (GNUP-Fs), generalized neutrosophic UP-ideals (GNUP-Is) and generalized neutrosophic strong UP-ideals (GNUP-SIs) in UP-algebras and investigate some related properties. Furthermore, the relationship between these five types of algebraic substructures in UP-algebras is discussed. After that, the conditions under which GNUP-S can be GNNUP-F, and the condition under which GNUP-F can be GNUP-I in UP-algebra are discovered. At last, a number of characterizations theorems of our concepts are presented and proved.

    How to Cite

    M. Alqahtani, M. Abuqamar, A. Al-Masarwah, A Proposed Method for Establishing Five Algebraic Substructures in UP-Algebras in View of Generalized Neutrosophic Structures, Int. J. Anal. Appl. 23 (2025), 279. https://doi.org/10.28924/2291-8639-23-2025-279

    BibTeX
    @article{Alqahtani2025,
  author  = {Alqahtani, Mohammed and Abuqamar, Majdoleen and Al-Masarwah, Anas},
  title   = {A Proposed Method for Establishing Five Algebraic Substructures in UP-Algebras in View of Generalized Neutrosophic Structures},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {279},
  doi     = {10.28924/2291-8639-23-2025-279}
}

    References

    • [1] K. Iséki, An Algebra Related with a Propositional Calculus, Proc. Jpn. Acad. Ser. Math. Sci. 42 (1966), 26–29. https://doi.org/10.3792/pja/1195522171.
    • [2] C. Prabpayak, U. Leerawat, On Ideals and Congruences in KU-Algebras, Sci. Magna 5 (2009), 54–57.
    • [3] A. Iampan, A New Branch of the Logical Algebra: UP-Algebras, J. Algebr. Relat. Top. 5 (2017), 35–54. https://doi.org/10.22124/jart.2017.2403.
    • [4] A. Iampan, Multipliers and Near Up-Filters of Up-Algebras, J. Discret. Math. Sci. Cryptogr. 24 (2019), 667–680. https://doi.org/10.1080/09720529.2019.1649027.
    • [5] L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
    • [6] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy Sets in UP-Algebras, Ann. Fuzzy Math. Inform. 12 (2016), 739–756.
    • [7] 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.
    • [8] W. Kaijae, P. Poungsumpao, S. Arayarangsi, A. Iampan, UP-algebras Characterized by Their Anti-Fuzzy UP-ideals and Anti-Fuzzy UP-Subalgebras, Ital. J. Pure Appl. Math. 36 (2016), 667–692.
    • [9] K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/s0165-0114(86)80034-3.
    • [10] B. Kesorn, K. Maimun, W. Ratbandan, A. Iampan, Intuitionistic Fuzzy Sets in UP-Algebras, Ital. J. Pure Appl. Math. 34 (2015), 339–364.
    • [11] N. Rajesh, T. Oner, A. Iampan, I. Senturk, Intuitionistic Fuzzy Structures on Sheffer Stroke UP-Algebras, Eur. J. Pure Appl. Math. 18 (2025), 5627. https://doi.org/10.29020/nybg.ejpam.v18i1.5627.
    • [12] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, (1999).
    • [13] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single Valued Neutrosophic Sets, Infinite Study, 2010.
    • [14] M. Songsaeng, A. Iampan, Neutrosophic Set Theory Applied to Up-Algebras, Eur. J. Pure Appl. Math. 12 (2019), 1382–1409. https://doi.org/10.29020/nybg.ejpam.v12i4.3543.
    • [15] H.S. Hasan, M.M. Salih, A.B. Khalaf, A Study on Neutrosophic Up-Algebra, Int. J. Neutrosophic Sci. 26 (2025), 67–77. https://doi.org/10.54216/ijns.260207.
    • [16] M. Songsaeng, A. Iampan, A Novel Approach to Neutrosophic Sets in Up-Algebras, J. Math. Comput. Sci. 21 (2020), 78–98. https://doi.org/10.22436/jmcs.021.01.08.
    • [17] S.Z. Song, M. Khan, F. Smarandache, Y.B. Jun, a Novel Extension of Neutrosophic Sets and Its Application in BCK/BCI-Algebras, Infinite Study, (2018).
    • [18] R.A. Borzooei, X. Zhang, F. Smarandache, Y.B. Jun, Commutative Generalized Neutrosophic Ideals in BCK-Algebras, Symmetry 10 (2018), 350. https://doi.org/10.3390/sym10080350.
    • [19] A. Iampan, Introducing Fully Up-Semigroups, Discuss. Math. - Gen. Algebr. Appl. 38 (2018), 297–306. https://doi.org/10.7151/dmgaa.1290.