Some Maclaurin Symmetric Mean Operators Based on Neutrosophic Linguistic Numbers for Multi-Attribute Group Decision Making

Abstract. Neutrosophic linguistic numbers (NLNs) can depict the uncertain and imperfect information by linguistic variables (LVs). As the classical aggregation operator, the Maclaurin symmetric mean (MSM) operator has its prominent characteristic that reflects the interactions among multiple attributes. Considering such circumstance: there are interrelationship among the attributes which take the forms of NLNs and the attribute weights are fully unknown in multiple attribute group decision making (MAGDM) problems, we propose a novel MAGDM methods with NLNs. Firstly, the MSM is extended to NLNs, that is, aggregating neutrosophic linguistic information by two new operators – the NLN Maclaurin symmetric mean (NLNMSM) operator and the weighted NLN Maclaurin symmetric mean (WNLNMSM) operator. Then, we discuss some characteristics and detail some special examples of the developed operators. Further, we develop an information entropy measure under NLNs to assign the objective weights of the attributes. Based on the entropy weights and the proposed operators, an approach to MAGDM problems with NLNs is introduced. Finally, a manufacturing industry example is given to demonstrate the effectiveness and superiority of the proposed method.