Skeleton-based action recognition using graph convolutional networks has attracted significant attention due to its simplicity and robustness. However, relying solely on skeleton-based information inevitably leads to losing information about the objects with which the character interacts. Therefore, maximizing implicit information between joints and bones to capture subtle differences in actions remains a significant challenge. To address these issues, a fuzzy action recognition algorithm for fusing rigid skeletal nodes to graph convolutional networks is proposed. First, rigid skeletal nodes are selected as center-of-mass nodes to construct the topology graph. Second, a distance classification attention topology network is developed to generate three distinct topology graph structures. This method effectively groups joints with similar semantic characteristics into the same set, accounting for direct skeletal connections and implicit relationships between more distant joints. Moreover, a skip connection module is integrated into the network to facilitate the reuse of key information during training. Finally, a fuzzy action calibration module is introduced to enhance the clustering of confident samples by decoupling features in both spatial and temporal domains, thereby learning subtle differential representations of fuzzy actions through contrastive learning. Our model is evaluated on three public datasets: NTU RGB+D, NTU RGB+D 120, and NW-UCLA. It achieves an accuracy of 93.1 \(\% \) on the X-Sub subset of the NTU RGB+D dataset, 90.1 \(\%\) on the X-Sub subset of the NTU RGB+D120 dataset, 91.7 \(\%\) on the X-Set subset, and 97.0 \(\%\) on the NW-UCLA dataset, demonstrating a significant advantage over state-of-the-art methods.