Circular spherical fuzzy aggregation operators: A case study of risk assessments on industry expansion

The circular spherical fuzzy set (C-SFS), an advanced concept that integrates the features of picture fuzzy sets (PFS) and spherical fuzzy sets, is presented in this work. Previous models often lack the flexibility and capacity to effectively handle intricate uncertainties and ambiguous data due to limited parameters and constrained frameworks. To address these limitations, the C-SFS model enhances the representation and analysis of imprecise data by introducing additional parameters and amore robust structure. The study aims to provide a comprehensive framework for managing ambiguity and uncertainty in decision-making. Specifically, we explore various aggregation operators within the C-SFS framework and thoroughly evaluate their mathematical properties, such as norms and co-norms. The practical applicability of these operators is illustrated through a case study on risk assessment in manufacturing, demonstrating their ability to integrate multiple factors and resolve complex uncertainties. Comparative analysis further reveals that the C-SFS framework outperforms traditional approaches in ambiguity handling and decision-making efficacy. These findings contribute significantly to fuzzy set theory by offering an innovative method for multi-criteria decision- making with broad potential applications. The study establishes a strong foundation for future research and practical implementations of C-SFS in addressing real-world challenges involving uncertainty and complexity.