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As an unsupervised ensemble learning strategy, clustering ensemble combines multiple base clusterings into a high-quality one and has achieved successful applications in image analysis and data mining. However, extant clustering ensemble methods are ineffective to handle the data uncertainty in clustering consensus process, which may mislead to poor clustering ensemble results. To tackle the problem, we propose a stable clustering ensemble (SCE) method based on evidence theory (Dempster-Shafer theory) in this paper. Specifically, we construct a belief function of cluster membership to measure the uncertainty and stability of data instances in clustering ensemble and thereby implement the stable clustering ensemble algorithm. We test the proposed stable clustering ensemble method in the tasks of structural data clustering and image segmentation. The experimental results validate the proposed method is effective to process the uncertain data and produce high-quality data clusterings.