The ability of q-rung dual hesitant fuzzy sets (q-RDHFSs) in dealing with decision makers’ fuzzy evaluation information has received much attention. This main aim of this paper is to propose new aggregation operators of q-rung dual hesitant fuzzy elements and employ them in multi-attribute decision making (MADM). In order to do this, we first propose the power dual Maclaurin symmetric mean (PDMSM) operator by integrating the power geometric (PG) operator and the dual Maclaurin symmetric mean (DMSM). The PG operator can reduce or eliminate the negative influence of decision makers’ extreme evaluation values, making the final decision results more reasonable. The DMSM captures the interrelationship among multiple attributes. The PDMSM takes the advantages of both PG and DMSM and hence it is suitable and powerful to fuse decision information. Further, we extend the PDMSM operator to q-RDHFSs and propose q-rung dual hesitant fuzzy PDMSM operator and its weighted form. Properties of these operators are investigated. Afterwards, a new MADM method under q-RDHFSs is proposed on the basis on the new operators. Finally, the effectiveness of the new method is testified through numerical examples.

This paper aims to propose a new multi-attribute decision making (MADM) method in complicated and fuzzy decision-making environment. To express both decision makers (DMs’) quantitative and qualitative evaluation information comprehensively and consider their high hesitancy in giving their assessment values in MADM process, we combine q-rung dual hesitant fuzzy sets (q-RDHFSs) with uncertain linguistic variables and develop a new tool, called the q-rung dual hesitant uncertain linguistic sets (q-RDHULSs). First, the definition, operations and comparison method of q-RDHULSs are proposed. Second, given the interrelationship among multiple q-rung dual hesitant uncertain linguistic variables (q-RDHULVs) we introduce some aggregation operators (AOs) to fuse q-rung dual hesitant uncertain linguistic (q-RDHUL) information based on the Muirhead mean, i.e. the q-RDHUL Muirhead mean operator, the q- RDHUL weighted Muirhead mean operator, the q-RDHUL dual Muirhead mean operator, and the q-RDHUL weighted dual Muirhead mean operator. To cope with MADM problems with q-RDHUL information, we propose a new method based on the proposed AOs. Afterwards, we apply the proposed method to an enterprise informatization level evaluation problem to verify its effectiveness. In addition, we also explain why our proposed method is more powerful and flexible than others.