Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application

T.; J.; S. John; D.

doi:https://doi.org/10.54216/IJNS.260104

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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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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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[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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