Fermatean Probabilistic Hesitant Fuzzy Power Bonferroni Aggregation Operators with Dual Probabilistic Information and Their Application in Green Supplier Selection

Abstract

In the realm of management decision-making, the selection of green suppliers has long been a complex issue. Companies must take a holistic approach, evaluating potential suppliers based on their capabilities, economic viability, and environmental impact. The decision-making process, fraught with intricacies and uncertainties, urgently demands the development of a scientifically sound and efficient method for guidance. Since the concept of Fermatean fuzzy sets (FFSs) was proposed, it has been proved to be an effective tool for solving multi-attribute decision-making (MADM) problems in complicated realistic situations. And the Power Bonferroni mean (PBM) operator, combining the strengths of the power average (PA) and Bonferroni mean (BM), excels in considering attribute interactions for a thorough evaluation. To ensure a comprehensive and sufficient evaluation framework for supplier selection, this paper introduces innovative aggregation operators that extend the PBM and integrate probabilistic information into Fermatean hesitant fuzzy sets (FHFSs) and Fermatean probabilistic hesitant fuzzy sets (FPHFSs). It successively proposes the Fermatean hesitant fuzzy power Bonferroni mean (FHFPBM), Fermatean hesitant fuzzy weighted power Bonferroni mean (FHFWPBM), and Fermatean hesitant fuzzy probabilistic weighted power Bonferroni mean (FHFPWPBM) operators, examining their key properties like idempotency, boundedness, and permutation invariance. By further integrating PBM with probabilistic information into FPHFSs, three new Fermatean probabilistic hesitant fuzzy power Bonferroni aggregation operators are developed: the Fermatean probabilistic hesitant fuzzy power Bonferroni mean (FPHFPBM), Fermatean probabilistic hesitant fuzzy weighted power Bonferroni mean (FPHFWPBM), and Fermatean probabilistic hesitant fuzzy probabilistic weighted power Bonferroni mean (FPHFPWPBM). Subsequently, a MADM method based on these operators is constructed. Finally, a numerical example concerning the selection of green suppliers is presented to demonstrate the applicability and effectiveness of this method using the FPHFPWPBM operator.