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Existing multi-view classification algorithms focus on promoting accuracy by exploiting different views, typically integrating them into common representations for follow-up tasks. Although effective, it is also crucial to ensure the reliability of both the multi-view integration and the final decision, especially for noisy, corrupted and out-of-distribution data. Dynamically assessing the trustworthiness of each view for different samples could provide reliable integration. This can be achieved through uncertainty estimation. With this in mind, we propose a novel multi-view classification algorithm, termed trusted multi-view classification (TMC), providing a new paradigm for multi-view learning by dynamically integrating different views at an evidence level. The proposed TMC can promote classification reliability by considering evidence from each view. Specifically, we introduce the variational Dirichlet to characterize the distribution of the class probabilities, parameterized with evidence from different views and integrated with the Dempster-Shafer theory. The unified learning framework induces accurate uncertainty and accordingly endows the model with both reliability and robustness against possible noise or corruption. Both theoretical and experimental results validate the effectiveness of the proposed model in accuracy, robustness and trustworthiness.