In today ’ s world, the demand for sustainable third-party reverse logistics providers (S3PRLPs) becomes an increasingly considerable issue for industries seeking improved customer service, cost reduction and sustainability perspectives . However, the assessment and selection of right S3PRLP is a complex uncertain decision-making problem due to involvement of numerous conflicting attributes, imprecise human mind and lack of information . Recently, Fermatean fuzzy set (FFS) has been recognized as one of the suitable tools to tackle the uncertain and inaccurate information . In this paper, we introduce a hybrid methodology based on CRITIC and EDAS methods with Fermatean fuzzy sets (FFSs) to solve the S3PRLP selection problem in which the attributes and decision makers ’ weights are completely unknown . In this framework, CRITIC approach is applied to calculate the attribute weight and EDAS method is used to evaluate the priority order of S3PRLP options . To do this, a new improved generalized score function (IGSF) is developed with its elegant properties . Also, a formula is discussed to calculate the decision makers ’ weights based on the developed IGSF . Next, developed framework is applied to assess a case study of S3PRLP selection problem with Fermatean fuzzy information, which elucidates the usefulness and practicality of the proposed method . Finally, comparative study is implemented to show the strength of introduced framework with extant approaches . The outcomes of the work confirm that the introduced approach is more feasible and well-consistent with the other extant approaches.