Volume 23 • Issue 3 • PP: 304-317 • 2024
Neutrosophic ideals of several types in UP (BCC)-algebras
Open Access & Copyright
© 2024 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
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
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
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.