Bonferroni Mean-Based Aggregation Operators on q-Rung Picture Fuzzy Sets for Multi-Criteria Decision Making in Energy Storage Systems

Selecting the right energy storage system (ESS) for grid integration is a high-stakes decision involving conflicting technical, economic, environmental, and risk criteria under deep uncertainty. The existing fuzzy multi-criteria decision-making (MCDM) methods either fail to capture neutral or abstaining expert judgments or treat evaluation criteria as independent, which is an unrealistic assumption in complex engineering decisions. To address both limitations simultaneously, this study develops four new aggregation operators by extending the Bonferroni mean (BM) into the q-rung picture fuzzy sets (q-RPFSs) framework: the q-RPFBM-based, q-RPFWBM-based, q-RPFGBM-based, and q-RPFWGBM-based operators. Unlike the existing q-RPFS operator families (Dombi, Frank, Fermatean, Yager, Maclaurin), which aggregate criteria independently, BM-based operators explicitly model pairwise interactions among criteria with a structurally distinct aggregation logic that is especially critical when criteria such as cost, risk, reliability, and environmental impact are mutually correlated. The theoretical validity of the operators is confirmed through proofs of idempotency, monotonicity, and boundedness. Applied to a comprehensive ESS selection problem for Türkiye (covering nine alternatives across nineteen sub-criteria and five main criteria, including an explicit risk dimension), the framework consistently identifies pumped hydro storage as the optimal choice. Sensitivity analyses under varying q, s, and t parameters, as well as perturbed criterion weights, confirm the robustness of this ranking. The proposed framework offers energy planners and decision-makers a principled and transparent tool for evaluating ESS under high uncertainty and criterion interdependence.