Power and Energy Transformation: Multi-Criteria Decision-Making Utilizing Complex q-Rung Picture Fuzzy Generalized Power Prioritized Yager Operators

Existing studies in decision-making often face limitations in adequately handling complex and uncertain environments. This study addresses these shortcomings by introducing novel operations and aggregation techniques tailored for complex q-rung picture fuzzy numbers (Cq-RPFNs). Building upon the drawbacks of conventional approaches, we extend Yager's operations to Cq-RPFNs, enabling comprehensive operations such as addition, multiplication, scalar product, and scalar power. Additionally, two aggregation operators—the Complex q-rung Picture Fuzzy Generalized Power Prioritized Yager Weighted Average and the Complex q-rung Picture Fuzzy Generalized Power Prioritized Yager Weighted Geometric—are developed to overcome the limitations of existing aggregation methods. Rigorous analysis of these operators for properties such as idempotency and monotonicity ensures their robustness in decision-making processes. Through a comprehensive multi-criteria decision-making method utilizing these operators, decision-makers are empowered to navigate complex decision landscapes effectively. Comparative evaluations against existing alternatives highlight the superiority and effectiveness of the proposed approaches. A case study focusing on India's Power and Energy Sector in 2024 demonstrates practical application, supported by numerical examples that validate the methodologies' efficacy. This study addresses the drawbacks of existing approaches and provides valuable insights and tools for decision-makers operating in complex and uncertain domains.