Some Frank Aggregation Operators for Interval-valued Intuitionistic Fuzzy Numbers and their Application to Group Decision Making

Frank t-conorm and t-norm are one important class of the t-conorm and t-norm with satisfying the compatibility, and can provide more flexible than other t-conorm and t-norm. In this paper, we extend Frank t-conorm and t-norm to interval-valued intuitionistic fuzzy numbers (IVIFNs), and define Frank operation rules of IVIFNs. Then, we propose interval-valued intuitionistic fuzzy Frank weighted averaging (IVIFFWA) operator and interval-valued intuitionistic fuzzy weighted geometric (IVIFFWG) operator, and discuss some desirable properties and some special cases of them. Furthermore, we apply these operators to multiple attribute group decision making (MAGDM) problems, and develop some new methods. Finally, an application example about air quality evaluation is given to demonstrate their practicality and effectiveness.