Nur Qasfareeny Abdul Halim1, Noor Azzah Awang 1,*, Nor Hashimah Sulaiman2, Hazwani Hashim3, Lazim Abdullah4
1School of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor, Malaysia
2School of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Dengkil Branch, 43800 Dengkil, Selangor, Malaysia
3School of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Kelantan Branch, 18500 Machang, Kelantan, Malaysia
4Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu (UMT), Kuala Nerus, 21030, Malaysia
Emails: qasfabdhalim@gmail.com; azzahawang@uitm.edu.my; norhashimah@uitm.edu.my; hazwani@uitm.edu.my lazim_m@umt.edu.my
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.
Keywords: Einstein operations; Rough neutrosophic set; Rough Neutrosophic Set Einstein operations; Multi-criteria decision-making