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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science
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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*
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,
S. Yamunadevi 2
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,
P. Maragatha Meenakshi 3
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,
N. Rajesh 4
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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
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© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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

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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
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