Adaptive Fermatean Fuzzy Sets: Theory, Aggregation Operators, and an Integrated Delphi–DEMATEL–MARCOS Decision Framework for Migration Policy Assessment

This study proposes a novel Adaptive Fermatean Fuzzy Set (AFFS) structure for multi-criteria decision-making problems characterized by high levels of uncertainty and hesitation in expert opinions. Unlike the fixed-exponent structure used in classical Fermatean fuzzy sets, the proposed model dynamically captures uncertainty based on the properties of alternatives by defining an adaptive exponent parameter for each assessment. In this context, new algebraic operations, a normalization approach, ranking mechanisms, distance and similarity measures, entropy-based information measures, and weighted aggregation operators have been developed for AFFS theory. Then, based on this theoretical structure, a new decision-making framework integrating the Adaptive Fermatean Fuzzy Delphi, DEMATEL, and MARCOS methods is proposed. The proposed approach allows for the determination of criterion weights and the more reliable ranking of alternatives by simultaneously considering expert consensus, information reliability, and uncertainty levels. The applicability of the method is demonstrated with a sample problem evaluating the impact of immigration policies on investment decisions. In the illustrative application, the largest criterion weight is assigned to Harmonization in Integration Policies (K3, w3=0.202687). The proposed AFF-MARCOS procedure yields A2 as the highest-ranked alternative with U2=0.722755, followed by A1, A4, A3, and A5.