Multi-attribute group decision making based on power generalized Heronian mean operator under hesitant fuzzy linguistic environment

Generalized Heronian mean (GHM) is a useful aggregation operator with the characteristic of capturing the interrelationship of evaluation information. In this paper, we propose some new operators by combining the power average operator and the GHM operator under hesitant fuzzy linguistic environment, such as the hesitant fuzzy linguistic power generalized Heronian mean (HFLPGHM) operator, the hesitant fuzzy linguistic power generalized geometric Heronian mean (HFLPGGHM) operator, the hesitant fuzzy linguistic weighted power generalized Heronian mean (HFLWPGHM) operator and the hesitant fuzzy linguistic weighted power generalized geometric Heronian mean (HFLWPGGHM) operator. Then, some special cases of the proposed HFLPGHM and HFLPGGHM operators are discussed in detail. Furthermore, based on the proposed operators, we develop a novel method to solve multi-attribute group decision-making problem under hesitant fuzzy linguistic environment. Finally, a numerical example is given to illustrate the application of the developed method and a comparison analysis is also conducted, which further demonstrates the effectiveness and feasibility of the proposed method.