| Gaia: | The concept of p,q− quasirung orthopair fuzzy (p,q− QOF) sets is an advanced extension of q− rung orthopair fuzzy sets (q− ROFSs). This paper introduces the adaptation of Hamacher t-norm and t-conorm to the p,q− QOF environment. A series of Hamacher aggregation operators (AOs) and their associated properties are presented. This study extends its application to multi-criteria group decision-making (MCGDM) for practical problem-solving, illustrated through the analysis of mobile payment platforms. The influence of the aggregation operator parameters, denoted as p and q, on the outcomes of decisions is effectively showcased. Moreover, a comparative analysis is carried out to validate the credibility and authenticity of the proposed model. Finally, the advantages and limitations of the proposed model are outlined.
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