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20261020111005
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International Journal of Neutrosophic Science
IJNS
2692-6148
2690-6805
2026
27
1
Some Einstein Operations on Rough Neutrosophic Sets with their Properties
Nur Qasfareeny Abdul
Halim
School of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor, Malaysia
Noor Azzah
Awang
School of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor, Malaysia
Nor Hashimah
Sulaiman
School of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Dengkil Branch, 43800 Dengkil, Selangor, Malaysia
Hazwani
Hashim
School of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Kelantan Branch, 18500 Machang, Kelantan, Malaysia
Lazim
Abdullah
Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu (UMT), Kuala Nerus, 21030, Malaysia
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Algebraic operations, which include addition, subtraction, division, scalar multiplication, and exponentiation, are the fundamental mathematical operations utilised in decision-making analysis. When performing on numbers, the algebraic operations are commonly referred to as arithmetic operations. Another alternative for algebraic operations, known as Einstein operations, has gained recognition for its smooth approximation and utilisation of Archimedean norms. However, it is crucial to note that Einstein operations are not designed to effectively address issues of indeterminacy, uncertainty, and lower-upper approximation. Thus, this paper defines some rough neutrosophic-based Einstein operations known as RNS Einstein addition, RNS Einstein multiplication, RNS Einstein scalar multiplication, and RNS Einstein exponentiation. By adopting rough neutrosophic sets (RNS), which incorporate neutrosophic lower and upper approximations, the proposed RNS Einstein operations offer a practical approach for handling uncertain situations. Some examples are provided to demonstrate the applicability of the RNS Einstein operations. Several desirable properties related to the defined RNS Einstein operations are investigated. Finally, the proposed RNS Einstein operations are applied in solving multi-criteria decision-making problems within a rough neutrosophic environment.
2026
43
58
3959
https://creativecommons.org/licenses/by/4.0/
10.54216/IJNS.270105
https://www.americaspg.com/journal/21/article/3959
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https://www.americaspg.com/storage/01753397184.pdf