Resolving conflicts is essential to make the decisions of multi-view classification more reliable. Much research has been conducted on learning consistent informative representations among different views, assuming that all views are identically important and strictly aligned. However, real-world multi-view data may not always conform to these assumptions, as some views may express distinct information. To address this issue, we develop a computational trust-based discounting method to enhance the existing trustworthy framework in scenarios where conflicts between different views may arise. Its belief fusion process considers the trustworthiness of predictions made by individual views via an instance-wise probability-sensitive trust discounting mechanism. We evaluate our method on six real-world datasets, using Top-1 Accuracy, AUC-ROC for Uncertainty-Aware Prediction, Fleiss' Kappa, and a new metric called Multi-View Agreement with Ground Truth that takes into consideration the ground truth labels. The experimental results show that computational trust can effectively resolve conflicts, paving the way for more reliable multi-view classification models in real-world applications.