A Novel Multi-attribute Group Decision-Making Method Under Linguistic q-Rung Orthopair Fuzzy Environment Based on Archimedean Copula and Extended Power Average Operator

Multi-attribute group decision-making (MAGDM) refers to a series of decision-making problems that rank all possible alternatives based on decision makers' cognition and evaluations over alternatives from multiple attributes. Hence, the precondition of MAGDM is felicitously describing decision makers' fuzzy and uncertain cognitive information in complicated decision-making issues. The recently proposed linguistic q-rung orthopair fuzzy set (Lq-ROFS), which uses two linguistic terms to denote membership and non-membership degrees, has been proved to be an effective and promising tool to depict decision makers' complex cognition in real MAGDM problems. Considering the drawbacks of existing Lq-ROFS-based decision-making methods, this paper focuses on MAGDM approaches where decision makers' cognitive information is denoted by Lq-ROFSs. The main contribution of this paper is to propose a novel MAGDM method based on Lq-ROFSs. This paper introduces a new MAGDM method under Lq-ROFSs. In order to do this, this study first puts forward some new operational rules for linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) based on Archimedean copula. These new operational rules are more flexible than existing ones and some other operations can be derived by using different generators. Second, to effectively aggregate Lq-ROFNs, the extended power average operator is applied in linguistic q-rung orthopair fuzzy environment and based on the new operational rules, some novel aggregation operators are generated. Afterward, the developed aggregation operators are used in decision-making problems and a novel MAGDM method which concentrates on linguistic q-rung orthopair fuzzy decision environment is introduced. Specific steps of the new method are illustrated in detail and it is then applied in some illustrative examples to verify its effectiveness. Our proposed method is effective for handling MAGDM problems under Lq-ROFSs. Numerical examples have shown the effectiveness in handling realistic MAGDM problems. In addition, comparison with some existing methods illustrates the advantages and superiorities of our method. This paper introduces a new MAGDM method under Lq-ROFSs. This method is based on Archimedean copula, extended power average operator, and Lq-ROFSs, and is powerful and flexible to cope with MAGDM problems in reality.