Some induced interval-valued Pythagorean trapezoidal fuzzy averaging aggregation operators based on Einstein operations and their application in group decision-making

Abstract

The aim of this paper is to investigate the information aggregation methods under interval-valued Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. We define interval-valued Pythagorean trapezoidal fuzzy aggregation operators, induced interval-valued Pythagorean trapezoidal fuzzy Einstein ordered weighted averaging (I-IVTFEOWA) operator and induced interval-valued Pythagorean trapezoidal fuzzy Einstein hybrid averaging (I-IVPTFEHA) operator. We discuss some basic properties of the proposed operator, including idempotency, commutativity and monotonicity. We construct an algorithm for multiple-attribute group decision-making problem, and apply the proposed aggregation operator to deal with multiple-attribute group decision-making. Finally, we construct a numerical example for multiple-attribute group decision-making.