The study is concerned with the representation and aggregation of complex uncertainty information. First, the concept of hesitant Fermatean 2-tuple linguistic sets (HF2TLSs) is introduced for characterizing an individual's imprecision preferences and assessing information by combining 2-tuple linguistic terms and Fermatean fuzzy sets. The advantage of hesitant Fermatean 2-tuple linguistic information is that it can handle higher levels of uncertainty and express the decision-makers' hesitancy.

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... econd, we extend Bonferroni mean (BM) operators under the background of HF2TLSs for the sake of their application in information fusion and decision making. The Archimedean t-norm and s-norm- (ATS-) based hesitant Fermatean 2-tuple linguistic weighted Bonferroni mean (A-HF2TLWBM) operator and the ATS-based hesitant Fermatean 2-tuple linguistic weighted geometric Bonferroni mean (A-HF2TLWGBM) operator are developed by considering the interrelationship between any two variables. The main benefit of the proposed operators is that these operators deliver more complete and flexible results compared to existing methods. Moreover, some fundamental properties and special cases are examined by adjusting parameter values. Finally, an approach is designed as a support for handling decision making problems, and an example regarding investment selection is provided to demonstrate the practicality of the designed method with a detailed discussion of parameter influence and comparisons with the existing methods.