Fermatean fuzzy geometric Bonferroni mean operator based decision support framework for green supplier selection

Abstract Now-a-days, many business organizations and companies are undertaking environmental considerations in supplier selection (SS) process due to growing environmental awareness and concern. Also choosing an appropriate green supplier (GS) will contribute to a company’s increased environmental sustainability. Sometimes it becomes very difficult to select the appropriate GS when a number of uncertainties present in selection process. So practical decision-making tools, like fuzzy sets (FSs) and its variants, those aim to address these issues are required to consider. In the present treatise, problem of GS selection (GSS) has been structured as a multi-criteria group decision making (MCGDM) problem under Fermatean fuzzy environment (FFE). For the first time, the notions of geometric Bonferroni mean operator (GBMO) and weighted GBMO (WGBMO) have been introduced under FFE to aggregate various decision maker’s (DM’s) assessments. Numerous salient traits of the proposed operators have been discussed theoretically as well as with numerical examples. To solve GSS problem, the notion of stepwise additive ratio analysis (SWARA) method has been extended under FFE with the aid of the proposed FFWGBMO to deal with group decision making issues under uncertainty. To rank the alternatives, FFWGBMO based novel ranking method has been developed and integrated with FFWGBMO based SWARA. A novel score function (SF) has been developed to rank Fermatean fuzzy numbers (FFNs), which is able to overcome the limitations of the existing FFSFs. The superiority of the proposed SF over the existing one has been validated through theoretical and numerical validations. Consistency, resilience and reliability of proposed integrated technique (PIT) have been investigated through comparative and sensitivity analyses.