Maclaurin symmetric means for linguistic Z-numbers and their application to multiple-attribute decision-making

Linguistic Z-Numbers (LZNs), as a more rational extension of linguistic description, consider the fuzzy restriction of assessment information and take the reliability of the information into account. Maclaurin Symmetric Mean (MSM) operator has the advantage which can take account of the interrelationship of dierent attributes and there are a lot of research results on it. However, it has not been used to handle Multi-Attribute Decision-Making (MADM) problems expressed by LZNs. To summarize the advantages of LZNs and MSM, in this article, we propose the Linguistic Z-number MSM (LZMSM) and Linguistic Z-number Weight MSM (LZWMSM) operators respectively, and several characters and special cases of them are discussed. In addition, we propose a method to deal with some MADM problems using the LZWMSM operator. Finally, by comparing it with several existing methods, an example is given to illustrate the eectiveness and superiority of this newly proposed method.