RETRACTED: Hesitant pythagorean fuzzy hamacher aggregation operators and their application to multiple attribute decision making (Retracted Article)

Hamacher product is a t-norm and Hamacher sum is a t-conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some hesitant Pythagorean fuzzy aggregation operators: hesitant Pythagorean fuzzy Hamacher weighted average (HPFHWA) operator, hesitant Pythagorean fuzzy Hamacher weighted geometric (HPFHWG) operator, hesitant Pythagorean fuzzy Hamacher ordered weighted average (HPFHOWA) operator, hesitant Pythagorean fuzzy Hamacher ordered weighted geometric (HPFHOWG) operator, hesitant Pythagorean fuzzy Hamacher hybrid average(HPFHHA) operator and hesitant Pythagorean fuzzy Hamacher hybrid geometric (HPFHHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.