Data with multiple uncertain labels are common in many situations. For examples, a movie may be associated with multiple genres with different levels of confidence, and a protein sequence may be probabilistically assigned to several structural subcategories. Despite their ubiquity, the problem of visualizing uncertain labels has not been adequately addressed. Existing approaches often either discard the uncertainty information, or map the data to a low-dimensional subspace where their associations with multiple labels are obscured. In this paper, we propose a novel visual mining technique, UnTangle, for visualizing uncertain multi-labels. In our proposed visualization, data items are placed inside a web of connected triangles, with labels assigned to the triangle vertices such that nearby labels are more relevant to each other. The positions of the data items are determined based on the probabilistic associations between items and labels. UnTangle provides both (a) an automatic label placement algorithm, and (b) adaptive interaction mechanisms that allow users to control the label positioning for different visual queries. Our work makes a unique contribution by providing an effective way to investigate the relationship between data items and their uncertain labels, as well as the relationships among labels. Our user study suggests that the visualization effectively helps users discover emergent patterns and compare the nuances of uncertainty information in the data labels.