<p>Effective decision-making in complex environments often requires handling fuzzy data with interdependencies. The generalized Heronian mean and geometric Heronian mean operators have proven useful for such analysis. However, existing methods struggle to capture correlations among pq-quasi rung orthopair fuzzy (pqQROF) numbers. This study addresses this gap by extending these operators to the pqQROF setting and developing a novel hybrid decision-making framework. The proposed framework integrates a distance measure, rank sum (RS) method, and aggregation operators to determine both objective and subjective criteria weights. The applicability of the approach is demonstrated through two case studies: project selection and university selection. Finally, a comparative evaluation of the developed operators against existing ones is conducted to assess their effectiveness and highlight the superiority of the proposed decision-making algorithm.</p>