Abstract
Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods.
Highlights
Smarandache [1] proposed the neutrosophic set (NS) in 1998
We establish the operation rules of Linguistic neutrosophic numbers (LNNs) based on Einstein operation and put forward the LNN Einstein weighted-average (LNNEWA)
We introduce two multiple attribute group decision making (MAGDM) methods with the LNNEWA or LNN Einstein weighted-geometry (LNNEWG) operator in
Summary
Smarandache [1] proposed the neutrosophic set (NS) in 1998. Compared with the intuitionistic fuzzy sets (IFSs), the NS increases the uncertainty measurement, from which decision makers can use the truth, uncertainty and falsity degrees to describe evaluation, respectively. The operators mentioned above are established based on the algebraic sum and the algebraic product of number sets They are respectively referred to as a special case of Archimedes t-conorm and t-norm to establish union or intersection operation of the number set. [27] put forward novel power aggregation operators based on Einstein operations for interval neutrosophic linguistic sets. It must be noticed that the aggregation operators in References [15,16,17,18] are almost based on the most commonly used algebraic product and algebraic sum of LNNs for carrying the combination process, which is not the only operation law that can be chosen to model the intersection and union on LNNs. we establish the operation rules of LNN based on Einstein operation and put forward the LNN Einstein weighted-average (LNNEWA).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
