Affiliations: [a] School of Economics and Management, Beijing Jiaotong University, Beijing, China
| [b] School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China
Correspondence:
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Corresponding author. Runtong Zhang, School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China. Tel.: +86 01051683854; E-mail: [email protected].
Abstract: The recently proposed q-rung orthopair fuzzy set (q-ROFS) is an effective tool for handling fuzziness and uncertainty in the process of multi-attribute group decision making (MAGDM). Considering that in most MAGDM problems, not only decision makers’ quantitative evaluation information but also their qualitative assessment opinions should be taken into account, this paper proposes a concept of q-rung orthopair uncertain linguistic sets (q-ROULSs) by combining q-ROFSs with uncertain linguistic variables (ULVs). The proposed q-ROULSs parallel to intuitionistic uncertain linguistic sets (IULSs) and Pythagorean uncertain linguistic sets (PULSs), but provide more freedom for decision makers to express their evaluation information. Afterwards, we propose operational laws and a comparison law for q-ROULSs. To effectively aggregate q-rung orthopair uncertain linguistic information, we extend the Muirhead mean (MM) operator to q-ROULSs and propose a family of q-rung orthopair uncertain linguistic Muirhead mean operators. The prominent advantage of the proposed operators is that the interrelationship among any numbers of input arguments can be captured. In addition, some desirable properties and special cases of the proposed operators are studied. Moreover, we propose a new method to MAGDM problems based on the proposed operators within q-rung orthopair uncertain linguistic context. Finally, we conduct a numerical experiment to demonstrate the validity and superiorities of the proposed method.
Keywords: q-rung orthopair fuzzy set, q-rung orthopair uncertain linguistic
set, Muirhead mean, q-rung orthopair uncertain linguistic Muirhead mean, multi-attribute group
decision making
