Fermatean hesitant fuzzy rough aggregation operators and their applications in multiple criteria group decision-making

The precise selection of suppliers to fulfill production requirements is a fundamental component of all manufacturing and process industries. Due to the increasing consumption levels, green supplier selection (GSS) has been one of the most important issues for environmental preservation and sustainable growth. The present work aims to develop a technique based on Fermatean hesitant fuzzy rough set (FHFRS), a robust fusion of Fermatean fuzzy set, hesitant fuzzy set, and rough set for GSS in the process industry. On the basis of the operational rules of FHFRS, a list of innovative Fermatean hesitant fuzzy rough weighted averaging operators has been established. Further, several intriguing features of the proposed operators are highlighted. To cope with the ambiguity and incompleteness of real-world decision-making (DM) challenges, a DM algorithm has been developed. To illustrate the applicability of the methodology, a numerical example for the chemical processing industry is presented to determine the optimum supplier. The empirical findings suggest that the model has a significant application of scalability for GSS in the process industry. Finally, the improved FHFR-VIKOR and TOPSIS approaches are employed to validate the proposed technique. The results demonstrate that the suggested DM approach is practicable, accessible, and beneficial for addressing uncertainty in DM problems.