Neutrosophic ideals of several types in UP (BCC)-algebras

V.; N.; Aiyared

doi:https://doi.org/10.54216/IJNS.230325

Full Length Article

Volume 23 • Issue 3 • PP: 304-317 • 2024

Neutrosophic ideals of several types in UP (BCC)-algebras

V. Rajam ^1*

mail

,

N. Rajesh ¹

mail

,

Aiyared Iampan ²

mail

¹Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur 613005, Tamilnadu, India

²Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.230325

format_quote Cite this article

Received: July 23, 2023 Revised: November 24, 2023 Accepted: February 23, 2024

View PDF open_in_new

Abstract

Characterizations of (∈,∈)-neutrosophic ideals and (q,∈ ∨q)-neutrosophic ideals are provided. Given special sets, so-called neutrosophic ∈-subsets, neutrosophic q-subsets, and neutrosophic (q,∈ ∨q)-subsets, conditions for the neutrosophic ∈-subsets, neutrosophic q-subsets, and neutrosophic (q,∈ ∨q)-subsets to be ideals are discussed.

Keywords

neutrosophic set (&isin &isin )-neutrosophic ideal (&isin q)-neutrosophic ideal (q &isin )-neutrosophic ideal (q &isin )-neutrosophic ideal (q &isin &or q)-neutrosophic ideal (q &isin &or q)-neutrosophic ideal.

References

[1] Y. Huang, BCI-algebra, Science Press, Beijing, China, 2006.

[2] A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top., 5(1), (2017), 35-54.

[3] Y. B. Jun, Neutrosophic subalgebras of several types in BCK/BCI-algebras, Ann. Fuzzy Math. Inform., 14(1), (2017), 75-86.

[4] Y. B. Jun, B. Brundha, N. Rajesh, and R. K. Bandaru, (3, 2)-Fuzzy UP (BCC)-subalgebras and (3, 2)- fuzzy UP (BCC)-filters, J. Mahani Math. Res. Cent., 11(3), (2022), 1-14.

[5] Y. Komori, The class of BCC-algebras is not a variety, Math. Japon., 29(3), (1984), 391-394.

[6] G. Muhiuddin, H. Bordbar, F. Smarandache, and Y. B. Jun, Further results on (∈,∈)-neutrosophic subalgebras and ideals in BCK/BCI-algebras, Neutrosophic Sets Syst., 20, (2018), 36-43.

[7] G. Muhiuddin and Y. B. Jun, Further results of neutrosophic subalgebras in BCK/BCI-algebras based on neutrosophic points, TWMS J. App. Eng. Math., 10(1), (2020), 232-240.

[8] M. A. Ozturk and Y. B. Jun, Neutrosophic ideals in BCK/BCI-algebras based on neutrosophic points, J. Int. Math. Virtual Inst., 8(1), (2018), 1-17.

[9] A. B. Saeid and Y. B. Jun, Neutrosophic subalgebras of BCK/BCI-algebras based on neutrosophic points, Ann. Fuzzy Math. Inform., 14(2), (2017), 87-97.

[10] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability (fourth edition), Rehoboth American Research Press, 2008.

[11] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24(3), (2005), 287-297.

[12] L. A. Zadeh, From circuit theory to system theory, Proc. Inst. Radio Eng., 50, (1962), 856-865.

[13] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), (1965), 338-353.

Cite This Article

Choose your preferred format

format_quote

Rajam, V., Rajesh, N., Iampan, Aiyared. "Neutrosophic ideals of several types in UP (BCC)-algebras." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, 2024, pp. 304-317. DOI: https://doi.org/10.54216/IJNS.230325

Rajam, V., Rajesh, N., Iampan, A. (2024). Neutrosophic ideals of several types in UP (BCC)-algebras. International Journal of Neutrosophic Science, Volume 23(Issue 3), 304-317. DOI: https://doi.org/10.54216/IJNS.230325

Rajam, V., Rajesh, N., Iampan, Aiyared. "Neutrosophic ideals of several types in UP (BCC)-algebras." International Journal of Neutrosophic Science Volume 23, no. Issue 3 (2024): 304-317. DOI: https://doi.org/10.54216/IJNS.230325

Rajam, V., Rajesh, N., Iampan, A. (2024) 'Neutrosophic ideals of several types in UP (BCC)-algebras', International Journal of Neutrosophic Science, Volume 23(Issue 3), pp. 304-317. DOI: https://doi.org/10.54216/IJNS.230325

Rajam V, Rajesh N, Iampan A. Neutrosophic ideals of several types in UP (BCC)-algebras. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 3):304-317. DOI: https://doi.org/10.54216/IJNS.230325

V. Rajam, N. Rajesh, A. Iampan, "Neutrosophic ideals of several types in UP (BCC)-algebras," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, pp. 304-317, 2024. DOI: https://doi.org/10.54216/IJNS.230325

Digital Archive Ready