Interval-valued picture fuzzy aggregation information based on Frank operators and their application in group decision making

The information aggregation operator plays a key rule in the multiple attribute group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the interval-valued picture fuzzy environment with the help of Frank norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely interval-valued picture fuzzy Frank weighted averaging operator, interval-valued picture fuzzy Frank ordered weighted averaging operator, interval-valued picture fuzzy Frank hybrid averaging operator, interval-valued picture fuzzy Frank weighted geometric operator, interval-valued picture fuzzy Frank ordered weighted geometric operator, and interval-valued picture fuzzy Frank hybrid geometric operator are proposed in this paper. Some general properties of these operators such as idempotency, commutativity, monotonicity, and boundedness, are discussed. Furthermore, the method for multiple attribute group decision making problems based on these operators is developed and the operational processes are illustrated in detail. Finally, an illustrative example has been given to show the decision steps of the proposed method and to demonstrate their effectiveness.