Volume 25 • Issue 3 • PP: 540-560 • 2025
Neutrosophic sets in IUP-algebras: a new exploration
Open Access & Copyright
© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
The notions of neutrosophic IUP-subalgebras, neutrosophic IUP-ideals, neutrosophic IUP-filters, and neutrosophic strong IUP-ideals of IUP-algebras are introduced, and their basic properties are investigated. Conditions for neutrosophic sets to be neutrosophic IUP-subalgebras, neutrosophic IUP-ideals, neutrosophic IUPfilters, and neutrosophic strong IUP-ideals of IUP-algebras are provided. Relations between neutrosophic IUP-subalgebras (resp., neutrosophic IUP-ideals, neutrosophic IUP-filters, neutrosophic strong IUP-ideals) and their level subsets are considered.
Keywords
References
[1] S. Al-Hijjawi and S. Alkhazaleh, Possibility neutrosophic hypersoft set (PNHSS), Neutrosophic Sets Syst., 53, (2023), 117–129.
[2] S. A. Alblowi, A. A. Salama, and M. Eisa, New concepts of neutrosophic sets, Int. J. Math. Comp. Appl. Res., 4, (2014), 95–102.
[3] S. Alias, D. Mohamad, and A. Shuib, Rough neutrosophic multisets, Neutrosophic Sets Syst., 16, (2017), 80–88.
[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20, (1986), 87–96.
[5] R. A. Borzooei, M. M. Takallo, F. Smarandache, and Y. B. Jun, Positive implicative BMBJ neutrosophic ideals in BCK-algebras, Neutrosophic Sets Syst., 23, (2018), 126–141.
[6] S. Broumi and F. Smarandache, Interval neutrosophic rough set, Neutrosophic Sets Syst., 7, (2015), 23–31.
[7] S. Broumi and F. Smarandache, Soft interval-valued neutrosophic rough sets, Neutrosophic Sets Syst., 7, (2015), 69–80.
[8] S. Broumi, F. Smarandache, and M. Dhar, Rough neutrosophic sets, Neutrosophic Sets Syst., 3, (2014), 60–65.
[9] C. Chanmanee, R. Prasertpong, P. Julatha, N. Lekkoksung, and A. Iampan, On external direct products of IUP-algebras, Int. J. Innov. Comput. Inf. Control, 19(3), (2023), 775–787.
[10] M. H. Hadi and L. A.A. Al-Swidi, The neutrosophic axial set theory, Neutrosophic Sets Syst., 51, (2022), 295–302.
[11] H. Hashim, L. Abdullah, and A. Al-Quran, Interval neutrosophic vague sets, Neutrosophic Sets Syst., 25, (2019), 66–75.
[12] A. Hussain and M. Shabir, Algebraic structures of neutrosophic soft sets, Neutrosophic Sets Syst., 7, (2015), 53–61.
[13] A. Iampan, P. Julatha, P. Khamrot, and D. A. Romano, Independent UP-algebras, J. Math. Comput. Sci., JMCS, 27(1), (2022), 65–76.
[14] J. James and S. C. Mathew, Lattice valued neutrosophic sets, J. Math. Comput. Sci., 11(4), (2021), 4695– 4710.
[15] M. Khan, F. Smarandache, and S. Afzal, Neutrosophic set approach for characterizations of left almost semigroups, Neutrosophic Sets Syst., 11, (2016), 79–94.
[16] K. Kuntama, P. Krongchai, R. Prasertpong, P. Julatha, and A. Iampan, Fuzzy set theory applied to IUPalgebras, J. Math. Comput. Sci., JMCS, 34(2), (2024), 128–143.
[17] A. Saha and S. Broumi, New operators on interval valued neutrosophic sets, Neutrosophic Sets Syst., 28, (2019), 128–137.
[18] A. A. Salama and F. Smarandache, Neutrosophic crisp set theory, Neutrosophic Sets Syst., 5, (2014), 27–35.
[19] A. A. Salama, F. Smarandache, and S. A. Alblowi, The characteristic function of a neutrosophic set, Neutrosophic Sets Syst., 3, (2014), 14–17.
[20] F. Smarandache, Neutrosophic set — a generalization of the intuitionistic fuzzy set, 2006 IEEE International Conference on Granular Computing, (2006), 38–42.
[21] F. Smarandache, Operators on single-valued neutrosophic oversets, neutrosophic undersets, and neutrosophic offsets, J. Math. Inf., 5, (2016), 67–67.
[22] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, and A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., 12(6), (2016), 739–756.
[23] S.-Z. Song, M. Khan, F. Smarandache, and Y. B. Jun, Interval neutrosophic sets applied to ideals in BCK/BCI-algebra, Neutrosophic Sets Syst., 18, (2017), 16–26.
[24] M. Songsaeng and A. Iampan, Neutrosophic set theory applied to UP-algebras, European J. Pure App. Math., 12(4), (2019), 1382–1409.
[25] M. Songsaeng and A. Iampan, Image and inverse image of neutrosophic cubic sets in UP-algebras under UP-homomorphisms, Int. J. Neutrosophic Sci., 3(2), (2020), 89–107.
[26] M. Songsaeng and A. Iampan, Neutrosophic cubic set theory applied to UP-algebras, Thai J. Math., 18(3), (2020), 1447–1474.
[27] M. Songsaeng and A. Iampan, A novel approach to neutrosophic sets in UP-algebras, J. Math. Comput. Sci., JMCS, 21(1), (2020), 78–98.
[28] M. Songsaeng, K. P. Shum, R. Chinram, and A. Iampan, Neutrosophic implicative UP-filters, neutrosophic comparative UP-filters, and neutrosophic shift UP-filters of UP-algebras, Neutrosophic Sets Syst., 47, (2021), 620–643.
[29] K. Suayngam, T. Suwanklang, P. Julatha, R. Prasertpong, and A. Iampan, New results on intuitionistic fuzzy sets in IUP-algebras, Int. J. Innov. Comput. Inf. Control, 20(4), (2024), 1125–1141.
[30] L. A. Zadeh, Fuzzy sets, Inf. Cont., 8(3), (1965), 338–353.
[31] X. Zhang, Y. Ma, and F. Smarandache, Neutrosophic regular filters and fuzzy regular filters in pseudo- BCI algebras, Neutrosophic Sets Syst., 17, (2017), 10–15.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.