A circular complex q-rung orthopair fuzzy framework for the large-scale optimization of renewable energy systems under uncertainty

Abstract Renewable energy system optimization has become increasingly challenging in modern energy networks due to the rapid integration of diverse renewable resources, large-scale operational requirements, complex interdependencies among energy components, and the presence of uncertain, incomplete, and imprecise information. Consequently, effective decision-making for renewable energy planning and optimization requires advanced analytical frameworks capable of simultaneously evaluating multiple, often conflicting, criteria, including energy efficiency, economic cost, environmental sustainability, resource availability, system reliability, operational flexibility, and technological feasibility. To address these challenges, this study introduces a novel Circular Complex q-Rung Orthopair Fuzzy (CrCq-ROF) framework, specifically designed to model uncertainty, ambiguity, and hesitation associated with large-scale renewable energy optimization problems. By integrating artificial intelligence techniques with the proposed fuzzy framework, the methodology enhances data-driven decision-making, improves predictive capability, and enables adaptive optimization under highly uncertain environments. Furthermore, several novel weighted averaging, ordered weighted averaging, weighted geometric, and ordered weighted geometric aggregation operators are developed based on newly established operational laws of Circular Complex q-Rung Orthopair Fuzzy information. Their fundamental mathematical properties and special cases are thoroughly investigated to demonstrate their validity, robustness, and flexibility for large-scale renewable energy applications. These aggregation operators are subsequently incorporated into the WASPAS multi-criteria decision-making methods to evaluate, rank, and optimize renewable energy alternatives under uncertain conditions. In addition, a group decision-making framework is proposed to integrate the preferences and judgments of multiple experts, thereby improving the consistency and reliability of the decision-making process. To validate the effectiveness of the proposed methodology, practical case studies involving large-scale renewable energy system optimization and renewable technology selection are presented. Comparative analyses and sensitivity investigations demonstrate that the proposed CrCq-ROF framework provides superior performance in handling uncertainty, complex-valued information, and conflicting evaluation criteria compared with existing approaches. Overall, the proposed methodology offers a flexible, robust, intelligent, and reliable decision-support framework for large-scale renewable energy system optimization under uncertain environments, thereby contributing to sustainable energy planning and informed strategic decision-making.