Optimizing biometric system selection via complex spherical fuzzy einstein aggregation operators

Biometric system evaluation in the banking sector involves significant uncertainty due to sensor reliability, environmental conditions, and user behavior variability. To address these challenges, this study employs a complex spherical fuzzy (CSF) framework that represents membership, neutrality, and non-membership information in a complex-valued form, enabling the simultaneous modeling of magnitude and phase characteristics. This makes CSF modeling particularly suitable for capturing time-dependent and cyclic performance patterns in biometric systems. Within this framework, two novel aggregation operators are introduced: the complex spherical fuzzy Einstein ordered weighted averaging (CSFEOWA) operator and the complex spherical fuzzy Einstein ordered weighted geometric (CSFEOWG) operator. By employing Einstein t-norm and t-conorm based aggregation, the proposed operators provide smooth and bounded nonlinear aggregation behavior that emphasizes joint performance and limits excessive compensation among criteria. Compared with classical linear aggregation operators, the proposed approach reduces sensitivity to extreme or unreliable inputs and yields more stable and balanced decision outcomes under uncertainty. Furthermore, an improved score function for complex spherical fuzzy numbers (CSFNs) is developed to ensure unambiguous ranking of alternatives. An MCDM algorithm based on the proposed operators is constructed and applied to the selection of an efficient biometric system for preventing financial mishaps in the banking sector. Comparative and sensitivity analyses demonstrate the robustness and practical effectiveness of the proposed framework, confirming its suitability for complex and uncertain decision-making scenarios.