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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science
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Volume 25 • Issue 3 • PP: 469-488 • 2025

Fermatean Neutrosophic Soft Set

Shawkat Alkhazaleh 1*
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,
Hamzeh Zureigat 1
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,
Belal Batiha 1
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,
Areen Al-khateeb 1
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,
Abedallah Al-shboul 1
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1Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.250339
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: March 28, 2024 Revised: June 27, 2024 Accepted: November 12, 2024
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Abstract

This paper aims to introduce a new concept which is Fermatean Neutrosophic Soft Set (FNSS), which is a combination of the Neutrosophic soft sets and Fermatean Fuzzy Sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of FNSS is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the most attractive laptop based on a computer simulation report. Finally, a comparative analysis between the initiated FNSS model and some existing approaches is provided to show its reliability.

Keywords

Fuzzy Set Soft Set Fuzzy Soft Set Fermatean Fuzzy Set Fermatean Fuzzy Soft Set Neutrosophic Set Neutrosophic Soft Set Fermatean Neutrosophic Set

References

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[2] Turksen, I. B. (1986). Interval valued fuzzy sets based on normal forms. Fuzzy sets and systems, 20(2), 191- 210.

[3] Atanassov, K. T. (1999). Intuitionistic fuzzy sets. In Intuitionistic fuzzy sets (pp. 1-137). Physica, Heidelberg.

[4] Neutrosophy, S. F. (1998). Neutrosophic probability, set, and logic, ProQuest Information & Learning. Ann Arbor, Michigan, USA, 105, 118-123.

[5] Smarandache, F. (2002). Neutrosophic set–a generalization of the intuitionistic fuzzy set. In University of New Mexico.

[6] Molodtsov, D. (1999). Soft set theory—first results. Computers & mathematics with applications, 37(4-5), 19- 31.

[7] Maji, P. K., Biswas, R. K., & Roy, A. (2001). Fuzzy soft sets.

[8] Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers & Mathematics with Applications, 45(4-5), 555-562.

[9] Majumdar, P., & Samanta, S. K. (2010). Generalised fuzzy soft sets. Computers & Mathematics with Applications, 59(4), 1425-1432.

[10] Sezgin, A., & Atagün, A. O. (2011). On operations of soft sets. Computers & Mathematics with Applications, 61(5), 1457-1467.

[11] Maji, P. K. (2013). Neutrosophic soft set. Infinite Study.

[12] Sahin, R., & Küçük, A. (2014). Generalised Neutrosophic Soft Set and its Integration to Decision Making Problem. Applied Mathematics & Information Sciences, 8(6).

[13] Broumi, S. (2013). Generalized neutrosophic soft set. Infinite Study.

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Alkhazaleh, Shawkat, Zureigat, Hamzeh, Batiha, Belal, Al-khateeb, Areen, Al-shboul, Abedallah. "Fermatean Neutrosophic Soft Set." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 3, 2025, pp. 469-488. DOI: https://doi.org/10.54216/IJNS.250339
Alkhazaleh, S., Zureigat, H., Batiha, B., Al-khateeb, A., Al-shboul, A. (2025). Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science, Volume 25(Issue 3), 469-488. DOI: https://doi.org/10.54216/IJNS.250339
Alkhazaleh, Shawkat, Zureigat, Hamzeh, Batiha, Belal, Al-khateeb, Areen, Al-shboul, Abedallah. "Fermatean Neutrosophic Soft Set." International Journal of Neutrosophic Science Volume 25, no. Issue 3 (2025): 469-488. DOI: https://doi.org/10.54216/IJNS.250339
Alkhazaleh, S., Zureigat, H., Batiha, B., Al-khateeb, A., Al-shboul, A. (2025) 'Fermatean Neutrosophic Soft Set', International Journal of Neutrosophic Science, Volume 25(Issue 3), pp. 469-488. DOI: https://doi.org/10.54216/IJNS.250339
Alkhazaleh S, Zureigat H, Batiha B, Al-khateeb A, Al-shboul A. Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 3):469-488. DOI: https://doi.org/10.54216/IJNS.250339
S. Alkhazaleh, H. Zureigat, B. Batiha, A. Al-khateeb, A. Al-shboul, "Fermatean Neutrosophic Soft Set," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 3, pp. 469-488, 2025. DOI: https://doi.org/10.54216/IJNS.250339
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