Pythagorean trapezoidal fuzzy geometric aggregation operators based on Einstein operations and their application in group decision making

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

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