A Bonferroni Mean Operator for p,q-Rung Triangular Orthopair Fuzzy Environments and Its Application in COPRAS Method

To broaden the informational scope of existing fuzzy frameworks and enhance their flexibility in representing and processing uncertainty, we propose a novel p,q-rung triangular orthopair fuzzy number (p,q-RTOFN). To enhance the aggregation capability of fuzzy data, we develop a p,q-rung triangular orthopair fuzzy weighted power Bonferroni mean (p,q-RTOFWPBM) operator that integrates the strengths of the Bonferroni mean and power average operators. We formally establish its theorems, proofs, and key properties, including symmetry and idempotency. Furthermore, we extend the complex proportional assessment (COPRAS) method to the p,q-RTOF environment, resulting in a p,q-RTOF-PBM-COPRAS model. This model effectively incorporates both positive and negative evaluation information under uncertainty, thereby reducing information loss and improving decision accuracy. A case study on urban smart farm selection confirms the feasibility and superiority of the proposed approach. This study introduces the p,q-RTOFN framework with extended informational scope, develops a hybrid p,q-RTOFWPBM operator, and incorporates these advances into an extended COPRAS method to achieve more accurate multi-criteria decision-making under uncertainty.