Some dual hesitant fuzzy Hamacher aggregation operators and their applications to multiple attribute decision making

In this paper, we extend the Hamacher operations to aggregate the dual hesitant fuzzy elements (DHFEs). Firstly, operational rules of DHFEs based on Hamacher t-norm and t-conorm are proposed. Then, we develop some dual hesitant fuzzy Hamacher aggregation operators based on the operational rules of DHFEs, such as dual hesitant fuzzy Hamacher weighted averaging (DHFHWA) operator, dual hesitant fuzzy Hamacher weighted geometric (DHFHWG) operator, dual hesitant fuzzy Hamacher ordered weighted averaging (DHFHOWA) operator, dual hesitant fuzzy Hamacher ordered weighted geometric (DHFHOWG) operator, dual hesitant fuzzy Hamacher hybrid averaging (DHFHHA) operator and dual hesitant fuzzy Hamacher hybrid geometric (DHFHHG) operator are proposed. Some desirable properties of these operators such as idempotency and boundedness are discussed, and some special cases of these operators are analyzed. Furthermore, a method to multiple attribute decision making (MADM) based on the proposed operators is developed. Finally, a practical example is given to illustrate the developed method and a comparison analysis is also conducted, which further demonstrates the practicality and effectiveness of the proposed approach.