In deep learning, local training methods often lead to overfitting and data silos due to privacy concerns and regulatory challenges. Federated learning addresses these issues by keeping data local and aggregating local models to update a global model. However, challenges like data heterogeneity and malicious client behaviors can degrade model performance, and fairness is often overlooked. This paper proposes a federated learning aggregation algorithm based on Shapley values, ensuring fairness by adjusting client weights and sampling strategies based on their marginal contributions. Using Shapley values and Monte Carlo sampling, the algorithm optimizes client weights, improving overall model performance while mitigating the impact of malicious clients and data heterogeneity. Experimental results on datasets like CIFAR-10 and Fashion MNIST demonstrate that the proposed algorithm balances fairness and effectiveness, outperforming traditional frameworks like Federated Averaging, Federated Proximal, and Collaborative Fairness in Federated Learning. This study provides an effective solution for federated learning in heterogeneous data environments, addressing fairness and robustness issues.