New approach to multiple attribute group decision-making based on Pythagorean fuzzy Einstein hybrid geometric operator

The objective of the present work is divided into two folds. Firstly, Pythagorean fuzzy Einstein hybrid geometric operator has been introduced along with their properties, namely idempotency, boundedness and monotonicity. Actually, Pythagorean fuzzy Einstein weighted geometric aggregation operator weighs only the Pythagorean fuzzy arguments, and Pythagorean fuzzy Einstein ordered weighted geometric aggregation operator weighs only the ordered positions of the Pythagorean fuzzy arguments instead of weighing the Pythagorean fuzzy arguments themselves. To overcome these limitations, we introduce the concept of Pythagorean fuzzy Einstein hybrid geometric aggregation operator, which weighs both the given Pythagorean fuzzy value and its ordered position. Thus, the main advantage of the proposed operator is that it is the generalization of their existing operators. Therefore, this method plays a vital role in real-world problems. Finally, we applied the proposed operator to multiple-attribute group decision-making.