Method of MAGDM based on pythagorean trapezoidal uncertain linguistic hesitant fuzzy aggregation operator with Einstein operations.

In this paper, we define some Einstein operations on Pythagorean trapezoidal uncertain linguistic hesitant fuzzy (PTULHF) set and developed Pythagorean trapezoidal uncertain linguistic hesitant fuzzy Einstein weighted geometric (PTULHFEWG) operator, Pythagorean trapezoidal uncertain linguistic hesitant fuzzy Einstein ordered weighted geometric (PTULHFEOWG) operator and Pythagorean trapezoidal uncertain linguistic hesitant fuzzy Einstein hybrid weighted geometric (PTULHFEHG) operator. Furthermore, we origin ate the relationship between the current aggregation operators and suggested operators and establish many properties of these operators. We apply the proposed aggregation operators to deal with multi-attribute group decision making (MAGDM) problems. Finally, an illustrative example is given to illustrate the decision-making steps and to demonstrate its practicality and effectiveness. We also compare the result of proposed method with existing methods.