A robust multigranulation-based circular complex Fermatean fuzzy framework for large-scale optimization of industrial safety response strategies under uncertain hazard risk conditions

Abstract Industrial safety management and hazard-response optimization have become increasingly challenging in modern large-scale industrial systems due to the growing complexity of manufacturing processes, interconnected operational environments, diverse hazard sources, and the presence of uncertain, incomplete, ambiguous, and imprecise information. Consequently, effective industrial safety planning and emergency response require advanced decision-making frameworks capable of simultaneously evaluating multiple, often conflicting, criteria, including hazard severity, operational reliability, response effectiveness, worker safety, environmental impact, resource allocation, system resilience, and mitigation efficiency. To address these challenges, this study introduces a novel Circular Complex Fermatean Fuzzy Set (CrC-FFS) framework, specifically designed to model uncertainty, ambiguity, hesitation, and complex-valued information associated with large-scale industrial hazard-risk assessment and safety management problems. The proposed Circular Complex Fermatean Fuzzy Set extends the capabilities of existing complex Fermatean fuzzy sets and circular Fermatean fuzzy sets by providing greater flexibility for representing higher-order uncertainty in practical industrial environments. Furthermore, several refined algebraic operational laws, including direct sum, direct product, and scalar multiplication based on generalized t-norms and t-conorms, are established to ensure consistent manipulation of Circular Complex Fermatean Fuzzy information. Based on these operational laws, novel weighted averaging, ordered weighted averaging, weighted geometric, and ordered weighted geometric aggregation operators are developed to effectively aggregate uncertain multi-criteria safety information. Their fundamental mathematical properties and special cases are thoroughly investigated to demonstrate their validity, robustness, and flexibility for industrial hazard-risk evaluation. These aggregation operators are subsequently incorporated into a multigranulation-based multi-criteria decision-making framework to prioritize hazard categories, evaluate mitigation strategies, optimize emergency response plans, and improve industrial safety performance under uncertain environments. To validate the effectiveness of the proposed methodology, a practical case study involving large-scale industrial hazard-risk assessment and safety response optimization is presented. Comparative analyses and sensitivity investigations demonstrate that the proposed CrC-FFS framework provides superior performance in handling uncertainty, complex-valued information, and conflicting safety criteria compared with existing approaches. Overall, the proposed methodology offers a flexible, robust, intelligent, and reliable decision-support framework for industrial safety management and hazard-response optimization under uncertain environments, thereby contributing to resilient industrial operations, improved risk mitigation, and informed strategic decision-making.