Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multi-input arguments. In this paper, we propose the dual Maclaurin symmetric mean (DMSM) operator and extend the DMSM operator to accommodate uncertain linguistic environment. Some new aggregation operators based on DMSM for aggregating uncertain linguistic information are developed, such as the uncertain linguistic dual Maclaurin symmetric mean (ULDMSM) operator, the uncertain linguistic weighted dual Maclaurin symmetric mean (ULWDMSM) operator and the uncertain linguistic Choquet dual Maclaurin symmetric mean (ULCDMSM) operator. Meanwhile, some desirable properties and special cases with respect to different parameter values of these operators are studied in detail. Furthermore, based on the ULWDMSM and ULCDMSM operators, two approaches to multiple attribute decision making with uncertain linguistic information are developed. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis with uncertain linguistic Bonferroni mean (ULBM) operator is also presented.