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, not only consider the fuzzy restriction of assessment information but also take the reliability of the information into account. Maclaurin symmetric mean (MSM) operator has the advantage which can take account of interrelationship of different 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 sum up the advantages of LZNs and MSM, in this paper, we present the linguistic Z-Numbers MSM (LZMSM) and linguistic Z-Numbers weight MSM (LZWMSM) operators, respectively, and several characters and several special cases of them are explored. Moreover, we propose an approach to handle some MADM problems by using LZWMSM operator. In the end, an example is given to illustrate the effectiveness and superiority of this new presented approach by comparing with several existing approaches.