Advances in Multi-Criteria Decision Making under Complex Spherical Fuzzy Environments: Algebraic Operations, Aggregation Operators and Supply Chain Applications

Rajendra Prasad, Tuan Nguyen

Handling high-dimensional epistemic uncertainty, cognitive ambiguity, and multi-dimensional subjectivity in complex engineering and managerial decision scenarios necessitates sophisticated fuzzy mathematical extensions. This paper introduces the theoretical foundations of Complex Spherical Fuzzy Sets (CSFS), which characterize membership, neutral, and non-membership grades within the unit sphere in the complex plane, capturing both degree and phase periodicity simultaneously. We define novel algebraic operational laws, score functions, and distance measures based on cosine similarity and geometric entropy. Furthermore, we develop a family of generalized Complex Spherical Fuzzy Weighted Averaging (CSFWA) and Geometric (CSFWG) aggregation operators and formally prove their idempotency, monotonicity, and boundedness properties. The proposed mathematical methodology is applied to resolve a sustainable green supplier selection problem in global semiconductor manufacturing under conflicting operational criteria. Comparative sensitivity analysis against traditional intuitionistic and Pythagorean fuzzy models demonstrates the superior expressiveness, mathematical robustness, and stability of the CSFS approach. Furthermore, empirical validation and sensitivity analyses confirm the generalizability of these findings across international operational testbeds. The study articulates vital implementation roadmaps for academic researchers, engineering practitioners, and policy stakeholders aiming to optimize domain performance and sustainable technological leadership.