Multi criteria group decision (MCGDM) for selecting third-party logistics provider (3PL) under Pythagorean fuzzy rough Einstein aggregators and entropy measures

In real life, with the trend of outsourcing logistics activities, choosing a third-party logistics (3PL) provider has become an inevitable choice for shippers. One of the most difficult decisions logistics consumers are facing the selecting the 3PL provider that best meets their needs. Decision making (DM) is an important in dealing with such situations because it allows them to make reliable decisions in a short period of time, as incorrect decisions can result in huge financial losses. In this regard, this article provides a new multi criteria group decision making method (MCGDM) under Pythagorean fuzzy rough (PyFR) set. A series of new PyFR Einstein weighted averaging aggregation operators and their basic aspects are described in depth. To evaluate the weights of decision experts and criteria weights we established the PyFR entropy measure. Further, using multiple aggregation methods based on PyFR information, a novel algorithm is offered to solve issues with ambiguous or insufficient data to obtain reliable and preferable results. First, decision-experts use PyFR sets to represent their evaluation information on alternatives based on the criteria. Then, apply all these proposed PyFR Einstein aggregation lists to rank all alternatives and find the best optimal result. Finally, to demonstrate the feasibility of the proposed PyFR decision system, a real example of choosing a 3PL is given.