A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets

Aiyared; S.; P. Maragatha; N.

doi:https://doi.org/10.54216/IJNS.200406

Full Length Article

Volume 20 • Issue 4 • PP: 78-92 • 2023

A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets

Aiyared Iampan ^1*

mail

,

S. Yamunadevi ²

mail

,

P. Maragatha Meenakshi ³

mail

,

N. Rajesh ⁴

mail

¹Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand

²Department of Mathematics, Vivekanandha College of Arts and Science for Women, Tiruchengode-637205, Tamilnadu, India

³Department of Mathematics, Periyar E.V.R. College (affiliated to Bharathidasan University), Tiruchirappalli-620023, Tamilnadu, India

⁴Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur-613005, Tamilnadu, India

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.200406

format_quote Cite this article

Received: January 09, 2023 Accepted: April 03, 2023

View PDF open_in_new

Abstract

In this paper, we introduce the concepts of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals of UP (BCC)-algebras. The characteristic neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals have also been studied. The relationshipbetween neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals and their level subsets is provided. The Cartesian product of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals.

Keywords

UP (BCC)-algebra neutrosophic hesitant fuzzy UP (BCC)-subalgebra neutrosophic hesitant fuzzy UP (BCC)-ideal neutrosophic hesitant fuzzy strong UP (BCC)-ideal.

References

[1] B. Ahmad, A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst., vol. 2009, Article ID: 586507, 6 pages, 2009.

[2] M. Atef, M. I. Ali, T. Al-shami, Fuzzy soft covering based multi-granulation fuzzy rough sets and their applications, Comput. Appl. Math., vol. 40, no. 4, Article number: 115, 2021.

[3] N. Caˇgman, S. Enginoˇglu, F. Citak, Fuzzy soft set theory and its application, Iran. J. Fuzzy Syst., vol. 8, no. 3, pp. 137-147, 2011.

[4] T. Guntasow, S. Sajak, A. Jomkham, A. Iampan, Fuzzy translations of a fuzzy set in UP-algebras, J. Indones. Math. Soc., vol. 23, no. 2, pp. 1-19, 2017.

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

[6] A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top., vol. 5, no. 1, pp. 35-54, 2017.

[7] Y. B. Jun, S. S. Ahn, G. Muhiuddin, Hesitant fuzzy soft subalgebra and ideal in BCI/BCK-algebras, Sci. World J., vol. 2014, Article ID: 763929, 7 pages, 2014.

[8] Y. B. Jun, B. Brundha, N. Rajesh, R. K. Bandaru, (3, 2)-Fuzzy UP (BCC)-subalgebras and (3, 2)-fuzzy UP (BCC)-filters, J. Mahani Math. Res. Cent., vol. 11, no. 3, pp. 1-14, 2022.

[9] Y. B. Jun, S.-Z. Song, Hesitant fuzzy set theory applied to filters in MTL-algebras, Honam Math. J., vol. 36, no. 4, pp. 813-830, 2014.

[10] Y. Komori, The class of BCC-algebras is not a variety, Math. Japon., vol. 29, no. 3, pp. 391-394, 1984.

[11] P. Mosrijai, W. Kamti, A. Satirad, A. Iampan, Hesitant fuzzy sets on UP-algebras, Konuralp J. Math., vol. 5, no. 2, pp. 268-280, 2017.

[12] J. Somjanta, N. Thuekaew, P. Kumpeangkeaw, A. Iampan, Fuzzy sets in UP-algebras, Ann. Fuzzy Math. Inform., vol. 12, no. 6, pp. 739-756, 2016.

[13] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., vol. 25, no. 6, pp. 529-539, 2010.

[14] V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, 18th IEEE Int. Conf. Fuzzy Syst., Jeju Island, pp. 1378-1382, 2009.

[15] L. A. Zadeh, Fuzzy sets, Inf. Control, vol. 8, no. 3, pp. 338-353, 1965.

[16] B. Zhu, Z. Xu, M. Xia, Dual hesitant fuzzy sets, J. Appl. Math., vol. 2012, Article ID: 879629, 13 pages, 2012.

Cite This Article

Choose your preferred format

format_quote

Iampan, Aiyared, Yamunadevi, S., Meenakshi, P. Maragatha, Rajesh, N.. "A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets." International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 4, 2023, pp. 78-92. DOI: https://doi.org/10.54216/IJNS.200406

Iampan, A., Yamunadevi, S., Meenakshi, P., Rajesh, N. (2023). A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets. International Journal of Neutrosophic Science, Volume 20(Issue 4), 78-92. DOI: https://doi.org/10.54216/IJNS.200406

Iampan, Aiyared, Yamunadevi, S., Meenakshi, P. Maragatha, Rajesh, N.. "A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets." International Journal of Neutrosophic Science Volume 20, no. Issue 4 (2023): 78-92. DOI: https://doi.org/10.54216/IJNS.200406

Iampan, A., Yamunadevi, S., Meenakshi, P., Rajesh, N. (2023) 'A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets', International Journal of Neutrosophic Science, Volume 20(Issue 4), pp. 78-92. DOI: https://doi.org/10.54216/IJNS.200406

Iampan A, Yamunadevi S, Meenakshi P, Rajesh N. A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets. International Journal of Neutrosophic Science. 2023;Volume 20(Issue 4):78-92. DOI: https://doi.org/10.54216/IJNS.200406

A. Iampan, S. Yamunadevi, P. Meenakshi, N. Rajesh, "A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets," International Journal of Neutrosophic Science, vol. Volume 20, no. Issue 4, pp. 78-92, 2023. DOI: https://doi.org/10.54216/IJNS.200406

Digital Archive Ready