Multiattribute Group Decision-Making Method in terms of Linguistic Neutrosophic Z-Number Weighted Aggregation Operators

To make a fuzzy value more reliable, Zadeh presented the notion of Z-number, which reflects a fuzzy value related to its reliability measure. Since linguistic expression conforms to human thinking habits, linguistic neutrosophic decision-making is one of the key research topics in linguistic indeterminate and inconsistent setting. In order to ensure the reliability of multiattribute group decision-making (MAGDM) problems in the linguistic environment of truth, falsehood, and indeterminacy, we require a new linguistic neutrosophic framework that combines the decision-maker’s linguistic neutrosophic judgment with its reliability measure. Inspired by the linguistic Z-numbers of the truth, falsehood, and indeterminacy, this article first proposes a linguistic neutrosophic Z-number (LNZN) to make the truth, falsehood, and indeterminacy linguistic values more reliable. Then, we define the operational relations, score and accuracy functions, and sorting laws of LNZNs. Next, we establish the LNZN weighted arithmetic mean (LNZNWAM) and LNZN weighted geometric mean (LNZNWGM) operators and indicate their properties. Furthermore, an MAGDM approach is developed based on the two aggregation operators and the score and accuracy functions of LNZNs in the LNZN setting. Lastly, an MAGDM example of industrial robot selection and comparison with existing related methods are provided to verify the applicability and efficiency of the developed MAGDM method in the setting of LNZNs. In general, the developed MAGDM approach not only makes the MAGDM information more reliable but also solves MAGDM problems under the environment of LNZNs.