<p>Rough set-based incremental attribute reduction is a competitive technique for knowledge acquisition. Incremental methods stand out by efficiently leveraging previously acquired knowledge to obtain new knowledge and thereby significantly reducing repetitive computations for dynamic data sets. Nevertheless, most of them primarily focus on complete decision systems, exhibiting a notable deficiency in handling missing information within incomplete decision systems. In addition, most existing research focuses on handling symbolic data, whereas practical applications often involve large amounts of real-valued data, posing greater challenges for attribute reduction. Drawing inspiration from these observations, we introduce a novel approach to handle dynamic real-valued data with features that contain missing values. Specifically, we define fuzzy granularity entropy for quantifying uncertainty of an incomplete real-valued decision system (IRDS), and explore its extensions such as joint granularity entropy and conditional granularity entropy. Furthermore, conditional granularity entropy is demonstrated to exhibit the desirable property of monotonicity. Moreover, the incremental mechanisms and corresponding algorithms are investigated for IRDS with variations in the number of objects. Finally, comparative experiments are carried out on different data sets to verify the effectiveness of the presented algorithms. Compared to the corresponding comparative methods, the results show that our approach achieves shorter reduct size, higher classification accuracy, and notably require less computing time.</p>