A novel group decision-making method for complex fuzzy information using extended power average operator and Frank operation

The interval-valued q-rung dual hesitant fuzzy sets (IVq-RDHFSs) has been proposed for effectively representing complex fuzzy information. IVq-RDHFSs can describe the membership degree and non-membership degree respectively through interval value set, and can flexibly adjust the space of information expression, which makes them surpass most existing fuzzy sets. Nevertheless, the main shortage of the existing multi-attribute group decision making (MAGDM) methods based on IVq-RDHFSs is that the functions of operation rules and aggregation operators (AOs) are very limited. Therefore, this paper investigates a new MAGDM under IVq-RDHFSs, established on the powerful Frank t-norm and t-conorm (FTT) operation and extended power average (EPA) operator. With the help of FTT, the basic operation of IVq-RDHFSs is redefined, then the interval-valued q-rung dual hesitant fuzzy Frank extended power average operator and the interval-valued q-rung dual hesitant fuzzy Frank weighted extended power average (IVq-RDHFFWEPA) operator are developed by combining FTT and EPA. Likewise, the desirable properties and special cases of the new AOs are explored. Afterwards, a novel MAGDM framework is constructed on the foundation of IVq-RDHFFWEPA operator. Compared with most existing approach, the proposed MAGDM in this paper possesses prominent ability in controlling the effect of extreme evaluation as well as modeling the risk attitude of decision-makers, so it is more appropriate for practical application. Finally, diverse experiments are devised to analyze the use and advantages of our method.