Interval-valued fermatean fuzzy sets with multi-criteria weighted aggregated sum product assessment-based decision analysis framework

Abstract

Fermatean fuzzy set, a generalization of the fuzzy set, is a significant way to tackle the complex uncertain information that arises in decision-analysis procedure and thus can be employed on a wider range of applications. Due to the inadequacy in accessible data, it is hard for decision experts to exactly define the belongingness grade (BG) and non-belongingness grade (NG) by crisp values. In such a situation, interval BG and interval NG are good selections. Thus, the aim of the study is to develop the doctrine of interval-valued Fermatean fuzzy sets (IVFFSs) and their fundamental operations. Next, the score and accuracy functions are proposed for interval-valued Fermatean fuzzy numbers (IVFFNs). Two aggregation operators (AOs) are developed for aggregating the IVFFSs information and discussed some axioms. Further, a weighted aggregated sum product assessment method for IVFFSs using developed AOs is introduced to handle the uncertain multi-criteria decision analysis problems. A case study of e-waste recycling partner selection is also considered to elucidate the feasibility and efficacy of the introduced framework. Finally, sensitivity and comparative analyses are given to elucidate the reliability and robustness of the obtained results.