提出可调控公平性的联邦学习框架，平衡全局与局部公平性。

With the emerging application of Federated Learning (FL) in decision-making scenarios, it is imperative to regulate model fairness to prevent disparities across sensitive groups (e.g., female, male). Current research predominantly focuses on two concepts of group fairness within FL: Global Fairness (overall model disparity across all clients) and Local Fairness (the disparity within each client). However, the non-decomposable, non-differentiable nature of fairness criteria poses two fundamental, unresolved challenges for fair FL: (i) Harmonizing global and local fairness, especially in multi-class setting; (ii) Enabling a controllable, optimal accuracy-fairness trade-off. To tackle these challenges, we propose a novel controllable federated group-fairness calibration framework, named FedFACT. FedFACT identifies the Bayes-optimal classifiers under both global and local fairness constraints, yielding models with minimal performance decline while guaranteeing fairness. Building on the characterization of the optimal fair classifiers, we reformulate fair federated learning as a personalized cost-sensitive learning problem for in-processing and a bi-level optimization for post-processing. Theoretically, we provide convergence and generalization guarantees for FedFACT to approach the near-optimal accuracy under given fairness levels. Extensive experiments on multiple datasets across various data heterogeneity demonstrate that FedFACT consistently outperforms baselines in balancing accuracy and global-local fairness.