Weight assignment is a universal and indispensable process in multi-view feature selection. However, most existing methods overlook the fuzziness and uncertainty implied in multi-view data. This may result in improper weight assignment, degrading the quality of selected features. A cross-view fuzziness and intra-view uncertainty-based weight reconstruction method (CFIUWR) is proposed for multi-view feature selection. With the fuzzy rough set theory, fuzzy approximation operators recognize cross-view fuzziness and intra-view uncertainty, which are evaluated by classification-related measurement. Cross-view fuzziness and intra-view uncertainty are incorporated to develop a reconstruction mechanism for view and feature weights. An optimization algorithm is derived, guaranteeing rapid convergence. Comparisons with state-of-the-art methods on several real-world datasets demonstrate the superiority of the CFIUWR.