Abstract
The interval-valued q-rung dual hesitant fuzzy sets (IVq-RDHFSs) effectively model decision makers’ (DMs’) evaluation information as well as their high hesitancy in complicated multi-attribute decision-making (MADM) situations. Note that the IVq-RDHFSs only depict DMs’ evaluation values quantificationally but overlook their qualitative decision information. To improve the performance of IVq-RDHFSs in dealing with fuzzy information, we incorporate the concept of uncertain linguistic variables (ULVs) into them and propose a new tool, called interval-valued q-rung dual hesitant uncertain linguistic sets (IVq-RDHULSs). Then we investigate MADM approach with interval-valued q-rung dual hesitant uncertain linguistic (IVq-RDHUL) information. Afterwards, the concept of IVq-RDHULSs as well as their operations and ranking method are proposed. Further, we propose a set of IVq-RDHUL aggregation operators (AOs) on the basis of the powerful Muirhead mean, i.e., the IVq-RDHUL Muirhead mean operator, the IVq-RDHUL weighted Muirhead mean operator, the IVq-RDHUL dual Muirhead mean operator, and the IVq-RDHUL weighted dual Muirhead mean operator. The significant properties of the proposed AOs are also discussed in detail. Lastly, we try to introduce a new method to MADM issues in IVq-RDHUL context based on the newly developed AOs.
Highlights
Multi-attribute decision-making (MADM) refers to a collection of decision-making problems that aim to select or determine the optimal or most suitable alternative(s) under multiple attributes
Some scholars studied MADM methods based on dual hesitant fuzzy aggregation operators (AOs) and we suggest readers to refer [25]–[35]
AGGREGATION OPERATORS FOR INTERVAL-VALUED Q-RUNG DUAL HESITANT UNCERTAIN LINGUISTIC INFORMATION we extend MM and dual Muirhead mean (DMM) to IVq-RDHUL environment and develop some IVq-RDHUL Muirhead mean AOs
Summary
Multi-attribute decision-making (MADM) refers to a collection of decision-making problems that aim to select or determine the optimal or most suitable alternative(s) under multiple attributes. 1) The MADM method proposed by Wei [36] is based on IVDHFULSs. The IVDHFULSs are constructed by interval-valued dual hesitant fuzzy uncertain linguistic numbers (IVDHFULNs), which satisfy the constraint that the sum of MD and NMD is less than or equal to one. 1) A new information representation tool, called interval-valued q-rung dual hesitant uncertain linguistic sets (IVq-RDHULSs), is proposed to depict DMs’ evaluation information. Remark 1: From the above definition, we know that the IVq-RDHULS is characterized by some interval-valued MDs and NMDs, with the constraint that the sum of qth power of MD and qth power of NMD is no more than one This characteristic makes IVq-RDHULSs powerful and flexible to express DMs’ evaluation information comprehensively.
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