Interval-valued fermatean fuzzy Aczel-Alsina geometric aggregation operators and their applications to group decision-making

Developing new aggregation operators on various classes of fuzzy sets and their generalizations is important in modelling real-life decision-making problems. Interval-valued Fermatean fuzzy sets (IVFFs) generalize the idea of interval-valued Pythagorean fuzzy sets (IVPFS) play a crucial role in modelling problems involving inadequate information. Decision-making problems modelled using IVFFNs require different score functions and aggregation operators on the set of IVFFNs. This study mainly focuses on establishing a few interval-valued Fermatean fuzzy (IVFF) aggregation operators by integrating the Aczel-Alsina (AA) operations to deal with group decision-making (GDM) problems. In this work, first, we discuss various Aczel-Alsina-based IVFF operations such as AA sum, AA product, and AA scalar multiplication for proposing a few new aggregation operators for the IVFF environment based on the new IVFF operations. Secondly, we introduce a few operators, including the interval-valued Fermatean fuzzy Aczel-Alsina (IVFFAA) weighted geometric operator, the IVFFAA ordered weighted geometric (IVFFAAOWG) operator, and the IVFFAA hybrid geometric (IVFFAAHG) operator. Various important properties such as idempotency, boundness, and monotonicity have also been studied. Thirdly, we establish multi-criteria group decision-making (MCGDM) method for solving real-life decision-making problems. Fourthly, we solve a model GDM problem to show the applicability and efficacy of our proposed MCGDM method, which utilizes the IVFFAAWG operator. Further, a sensitivity analysis is performed to ensure better performance, and finally, a comparative study of our method is done by comparing our proposed MCGDM approach with different existing methods.