In practical applications, due to the high cost of data labeling, some real-valued data are often only partially labeled, and such data can be processed using semi-supervised learning algorithms. For this scenario, this paper focuses on the fuzzy \(\beta \) -covering based partially labeled real-valued decision information system (F \(\beta \) -Cp-RVIS), investigates its uncertainty measurement problem and explores semi-supervised attribute reduction algorithms for real-valued data. Firstly, F \(\beta \) -Cp-RVIS is decomposed into two decision information systems: the fuzzy \(\beta \) -covering based labeled real-valued decision information system (F \(\beta \) -Cl-RVIS) and the fuzzy \(\beta \) -covering based unlabeled real-valued decision information system (F \(\beta \) -Cu-RVIS). Secondly, the importance of attribute subsets in F \(\beta \) -Cp-RVIS is defined based on the indiscernibility relation and conditional information entropy. This importance, obtained by weighted summation of F \(\beta \) -Cl-RVIS and F \(\beta \) -Cu-RVIS according to the missing rate, serves as the uncertainty measurement for F \(\beta \) -Cp-RVIS. Thirdly, experimental analyses and statistical tests on 12 datasets verify the effectiveness of the proposed uncertainty measurement. Based on this, an adaptive algorithm for F \(\beta \) -Cp-RVIS is proposed, which can automatically adapt to different missing rates. Finally, experimental and statistical results on 12 datasets show that the proposed algorithm significantly outperforms existing ones in classification accuracy.
