Arithmetic Aggregation Operators on Type-2 Picture Fuzzy Sets and Their Application in Decision Making

The aggregation operators are important tools in the process of information aggregation. The aim of this paper is to investigate arithmetic aggregation operators under the type 2 picture fuzzy environment with the help of new operations on type-2 picture fuzzy numbers. The type-2 picture fuzzy set is an extended version of Cuong's picture fuzzy set, which not only considers the degree of acceptance or rejection, but also takes into account the neutral degree and invalid degree during the analysis. Under these environments, by using the new operations on type-2 picture fuzzy numbers, several series of arithmetic aggregation operators for type-2 picture fuzzy sets are proposed, namely type-2 picture fuzzy weighted average operators, type-2 picture fuzzy ordered weighted average operators, and type-2 picture fuzzy hybrid average operators, along with their desirable properties. Furthermore, a decision-making approach based on these operators is also presented to make the evaluation result more objective. Finally, an illustrative example is provided to demonstrate the practicality and reasonableness of the proposed method.