Optimal discrete fitting aggregation approach with hesitant fuzzy information

As a novel and generalized fuzzy set, hesitant fuzzy set have received increasing attention and have been a popular research topic recently. However, many crossover calculations are needed to aggregate hesitant fuzzy information for multiple calculations in its general operation, whereas much more of these calculations are needed in hesitant fuzzy group decision making. This paper proposes optimal discrete fitting aggregation and simplified optimal discrete fitting aggregation as two new aggregation approaches to resolve this issue. The paper also distinguishes their similarities and differences, proves some desired properties, and provides the selected methods and modeling steps. Moreover, the length extended technology and the deviation function are developed as the applied basis of the new approaches. Two practical cases are provided at the end of this paper to demonstrate the application of the proposed approaches.