Affiliations: [a]
Department of Mathematics, Hazara University, Mansehra KPK, Pakistan
| [b]
Department of Mathematics, Abdul Wali Khan University, Mardan KPK, Pakistan
| [c]
Department of Electronics, University of Engineering and Technology, Taxila, Sub Campus Chakwal, Pakistan
Correspondence:
[*]
Corresponding author. Saleem.Abdullah, Department of Mathematics, Abdul Wali Khan University, Mardan KPK,
Pakistan. E-mail: saleemabdullah@awkum.edu.pk.
Abstract: The aim of this paper is to investigate information aggregation methods under Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Based on Einstein operations we define Pythagorean trapezoidal fuzzy Einstein weighted geometric (PTFEWG) operator, Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric (PTFEOWG) operator and Pythagorean trapezoidal fuzzy Einstein hybrid geometric (PTFEHG) operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making. In the last we construct a numerical example for multiple attribute group decision making problem and compare the result with existing method.
Keywords: Trapezoidal fuzzy numbers, pythagorean trapezoidal fuzzy numbers, Einstein operation, aggregation operation and group decision making
