To address the limitations of existing multi-source domain adaptation (MSDA) methods for fault diagnosis, which fail to adequately account for variations in source domain data quality, this paper proposes a trustworthy multi-source domain adaptation-based fault diagnosis (TMDAFD) model. First, an optimal common embedding space is constructed between the source and target domains to achieve effective feature alignment. Second, based on evidential deep learning theory, a domain adaptation model with uncertainty quantification is designed to measure the reliability of diagnostic results in the target domain under different source domain supports, providing a trustworthy basis for multi-source decision fusion. Finally, an information fusion strategy is designed based on the obtained uncertainty measure, which effectively integrates decision information from multiple source domains and consequently enhances the accuracy of cross-domain diagnosis. Experimental evaluations on rolling bearing fault datasets from Case Western Reserve University (CWRU), Jiangnan University (JNU), and the University of Ottawa (UO) demonstrate that the TMDAFD model significantly enhances the performance of cross-domain fault diagnosis tasks, validating its effectiveness in complex multi-source scenarios.