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.

Medical services inevitably generate healthcare waste (HCW) that may become hazardous to healthcare staffs, patients, the population, and the atmosphere. In most of the developing countries, HCW disposal management has become one of the fastest-growing challenges for urban municipalities and healthcare providers. Determining the location for HCW disposal centers is a relatively complex process due to the involvement of various alternatives, criteria, and strict government guidelines about the disposal of HCW. The objective of the paper is to introduce the WASPAS (weighted aggregated sum product assessment) method with Fermatean fuzzy sets (FFSs) for the HCW disposal location selection problem. This method combines the score function, entropy measure, and classical WASPAS approach within FFSs context. Next, a combined procedure using entropy and score function is proposed to estimate the criteria weights. To do this, a novel score function with its desirable properties and some entropy measures are introduced under the FFSs context. Further, an illustrative case study of the HCW disposal location selection problem on FFSs is established, which evidences the practicality and efficacy of the developed approach. Comparative discussion and sensitivity analysis are made to monitor the permanence of the introduced framework. The final results approve that the proposed methodology can effectively handle the ambiguity and inaccuracy in the decision-making procedure of HCW disposal location selection.