<p>Addressing the limitations of existing semi-supervised feature selection algorithms for partially labeled interval-valued information systems, this paper presents a novel solution. Firstly, to overcome the challenge of imprecise similarity measurements between interval-valued data, we have developed a novel similarity calculation formula that comprehensively considers three crucial factors: the interval overlap, centers, and width. Secondly, to address the issue where the evaluation of feature subset significance in the presence of missing labels fails to adapt to varying label missing rates, we construct an innovative feature subset significance index that incorporates the label missing rate. Furthermore, leveraging the mathematical properties of this significance index, we propose an simple feature selection rule. This rule streamlines the feature selection process by merely requiring a determination of whether the feature subset significance equals 1. Lastly, experiments conducted on both real-world and synthetic interval-valued datasets reveal that, compared with some cutting-edge methods, our algorithm achieves an average classification accuracy improvement of at least 6.14% and an average improvement in time efficiency of at least 3.40% on real-world interval-valued datasets, and enhancements of at least 5.73% and 5.41% in average classification accuracy and average clustering accuracy, respectively, on synthetic interval-valued datasets with added noise. Additionally, our algorithm exhibits stable performance across a range of label missing rates.</p>