A series of generalized induced Einstein aggregation operators and their application to group decision-making process based on Pythagorean fuzzy numbers

Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types induced Einstein aggregation operators namely, induced Pythagorean fuzzy Einstein ordered weighted averaging (I-PFEOWA) operator, induced Pythagorean fuzzy Einstein hybrid averaging (I-PFEHA) operator, induced generalized Pythagorean fuzzy Einstein ordered weighted averaging (I-GPFEOWA) operator, and induced generalized Pythagorean fuzzy Einstein hybrid averaging (I-GPFEHA) operator. Some desirable properties, such as idempotency, boundedness, and monotonicity corresponding to the proposed operators have been investigated. The main advantage of the proposed operators is that these operators are able to reflect the complex attitudinal character of the decision-maker using order inducing variables and provide much more complete information for decision-making. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach.