A Novel Group Decision-Making Method Based on Linguistic Neutrosophic Maclaurin Symmetric Mean (Revision IV)

Linguistic neutrosophic number (LNN) is a specific form of neutrosophic number whose elements are expressed by linguistic terms. Maclaurin symmetric mean (MSM) operator is one of the basic collection operators in the modern knowledge fusion theory. Its most important feature is to consider the interrelationships among multiple input arguments. Multiple attribute group decision-making (MAGDM) with linguistic neutrosophic information is considered. First, we present some basic concepts, then we combine the MSM operator with linguistic neutrosophic environment and develop a sequence of linguistic neutrosophic MSM operators which are the linguistic neutrosophic Maclaurin symmetric mean (LNMSM) operator, the weighted linguistic neutrosophic Maclaurin symmetric mean (WLNMSM) operator, linguistic neutrosophic dual Maclaurin symmetric mean (LNDMSM) operator, and the weighted linguistic neutrosophic dual Maclaurin symmetric mean (WLNDMSM) operator. We look into some features of them such as monotonicity, boundedness, and idempotency and then discuss some special situations of these operators. A new idea based on the WLNMSM operator is proposed to solve an MAGDM problem where evaluation information is composed of LNNs. It is worth mentioning that the weight information of the decision-makers (DMs) and the attributes are completely unknown. In conclusion, a comparison analysis is performed with the existing methods. The developed method is based on both the WLNMSM operator which considers the interrelationships among any number of input arguments and LNNs which is a combination of the neutrosophic numbers, linguistic variables. At the same time, it also has the advantages of mentioned components. So, it enables preventing the loss or distortion of the original decision information in the decision-making process. © 2020, Springer Science+Business Media, LLC, part of Springer Nature