<p>Semi-supervised outlier detection is a technique for analyzing outliers in data sets where label information is missing, specifically the labels that are necessary for categorizing or identifying data points. However, the majority of extant outlier detection methods eschew the use of label information, which may result in suboptimal detection outcomes. In practice, there is frequently a substantial corpus of numerical data with missing label information due to the challenges and high costs associated with data labeling. To overcome these issues, this paper presents a semi-supervised outlier detection approach based on generalized multi-granularity fuzzy neighborhood rough sets (GMFNRS) for numerical data with missing label information. Firstly, the value of the neighborhood parameter k is obtained adaptively through natural neighbor algorithm, which avoids the previous limitation of setting the neighborhood parameter in advance, and realizes the automation of the predictive labeling process of the k-nearest-neighbor-based label propagation algorithm. Secondly, to quantify the degree of anomaly in the granularity of objects with the same label, we propose the generalized multi-granularity fuzzy neighborhood outlier degree using the generalized multi-granularity fuzzy neighborhood approximation. Finally, the outlier score for each object is calculated by weighting the outlier degree and the corresponding outlier detection algorithm is proposed. We conduct experiments using ten publicly available datasets and perform experimental analysis. The experimental results show that the proposed algorithm outperforms some existing outlier detection algorithms.</p>