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Medical data widely exist in the hospital and personal life, usually across institutions and regions. They have essential diagnostic value and therapeutic significance. The disclosure of patient information causes people's panic, therefore, medical data security solution is very crucial for intelligent health care. The emergence of federated learning (FL) provides an effective solution, which only transmits model parameters, breaking through the bottleneck of medical data sharing, protecting data security, and avoiding economic losses. Meanwhile, the neural architecture search (NAS) has become a popular method to automatically search the optimal neural architecture for solving complex practical problems. However, few papers have combined the FL and NAS for simultaneous privacy protection and model architecture selection. Convolutional neural network (CNN) has outstanding performance in the image recognition field. Combining CNN and fuzzy rough sets can effectively improve the interpretability of deep neural networks. This article aims to develop a multiobjective convolutional interval type-2 fuzzy rough FL model based on NAS (CIT2FR-FL-NAS) for medical data security with an improved multiobjective evolutionary algorithm. We test the proposed framework on the LC25000 lung and colon histopathological image dataset. Experimental verification demonstrates that the designed multiobjective CIT2FR-FL-NAS framework can achieve high accuracy superior to state-of-the-art models and reduce network complexity under the condition of protecting medical data security.