A novel multiple attribute decision making method based on q-rung dual hesitant uncertain linguistic sets and Muirhead mean

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.