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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
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Volume 26 • Issue 1 • PP: 40-54 • 2025

Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application

T. Sathinathan 1*
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,
J. Aldring 2
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,
S. John Borg 1
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,
D. Ajay 1
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1PG and Research Department of Mathematics, Sacred Heart College, Tirupattur - 635601, India
2Department of Mathematics, Panimalar Engineering College, Poonamalle, Chennai -600123, India
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.260104
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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: November 05, 2024 Revised: January 03, 2025 Accepted: January 30, 2025
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Abstract

The objective of this paper is to present a perspective of Refined Neutrosophic Vector Space (r-NVS), Sub spaces and some basic operations on Refined Neutrosophic Sets such as Algebraic sum and Algebraic product. Further some basic propositions, lemma and examples are presented. Finally an application on Refined Neutrosophic Vector Space is presented in the field of e-Commerce buyer oriented product (Smart Phones) ranking to illustrate the advantage of representing r-NVS.

Keywords

Refined Neutrosophic Sets (r-NSs) Refined Neutrosophic Vector Space (r-NVS) Distance Measure MCDM

References

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[3] Smarandache, F. (2006). Neutrosophic set - a generalization of the intuitionistic fuzzy set. 2006 IEEE International Conference on Granular Computing, 38-42.

[4] Atanassov, K. (1983). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96.

[5] Deli, I., Broumi, S., & Smarandache, F. (2015). On neutrosophic refined sets and their applications in medical diagnosis. Journal of new theory, (6), 88-98.

[6] Agboola, A.A.A. On Refined Neutrosophic Algebraic Structures, Neutrosophic Sets and Systems, Vol. 10, pp 99-101, 2015

[7] Kandasamy, W. V., & Smarandache, F. (2004). Basic neutrosophic algebraic structures and their application to fuzzy and neutrosophic models (Vol. 4). Infinite Study.

[8] Malath. F. Aswad: n-Cyclic Refined Neutrosophic Vector Spaces and Matrices. Neutrosophic Knowledge, vol. 3/2021, pp. 6-13. DOI: 10.5281/zenodo.5507528

[9] Aswad, M. F. A Study of n-Refined Neutrosophic Complex Numbers and Their Properties. Neutrosophic Knowledge, Vol. 3, 2021

[10] Abobala, M. (2021). On the representation of neutrosophic matrices by neutrosophic linear transformations. Journal of Mathematics, 2021, 1-5. https://doi.org/10.1155/2021/5591576

[11] Rozina Ali. A Short Note On The Solution Of n-Refined Neutrosophic Linear Diophantine Equations. International Journal of Neutrosophic Science, 2021, https://dx.doi.org/10.5281/zenodo.4931677.

[12] A. M. Alzahrani, B. K. Alzahrani, and C. D. Smith, ”Refined Fuzzy Vector Spaces and Their Applications,” in *Journal of Mathematical Analysis and Applications*, vol. 500, pp. 1-15, 2021. DOI:

10.1016/j.jmaa.2021.124567.

[13] E. F. Johnson, G. H. Patel, and I. J. Kumar, ”Advanced Neutrosophic Models for Decision-Making Processes,” in *Applied Soft Computing*, vol. 112, pp. 1-10, 2022. DOI: 10.1016/j.asoc.2021.107853.

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Sathinathan, T., Aldring, J., Borg, S. John, Ajay, D.. "Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application." International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 1, 2025, pp. 40-54. DOI: https://doi.org/10.54216/IJNS.260104
Sathinathan, T., Aldring, J., Borg, S., Ajay, D. (2025). Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application. International Journal of Neutrosophic Science, Volume 26(Issue 1), 40-54. DOI: https://doi.org/10.54216/IJNS.260104
Sathinathan, T., Aldring, J., Borg, S. John, Ajay, D.. "Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application." International Journal of Neutrosophic Science Volume 26, no. Issue 1 (2025): 40-54. DOI: https://doi.org/10.54216/IJNS.260104
Sathinathan, T., Aldring, J., Borg, S., Ajay, D. (2025) 'Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application', International Journal of Neutrosophic Science, Volume 26(Issue 1), pp. 40-54. DOI: https://doi.org/10.54216/IJNS.260104
Sathinathan T, Aldring J, Borg S, Ajay D. Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application. International Journal of Neutrosophic Science. 2025;Volume 26(Issue 1):40-54. DOI: https://doi.org/10.54216/IJNS.260104
T. Sathinathan, J. Aldring, S. Borg, D. Ajay, "Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application," International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 1, pp. 40-54, 2025. DOI: https://doi.org/10.54216/IJNS.260104
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