Affiliations: [a] Department of Mathematics, Hazara Uinversity, Mansehra, Pakistan
| [b] Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia
| [c] Department of Information Technology, Hazara University, Mansehra, Pakistan
| [d] Department of Mathematics and Statistic, Riphah International University, Islamabad, Pakistan
Correspondence:
[]
Corresponding author. Muhammad Shakeel, Department of Mathematics, Hazara Uinversity, Mansehra, Pakistan. E-mail: Shakeel_maths@hu.edu.pk.
Abstract: 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.
Keywords: Trapezoidal fuzzy numbers, pythagorean trapezoidal fuzzy numbers, einstein operation, aggregation operation, multiple attribute group decision-making
