The existing methods have made preliminary progress in Uncertain Knowledge Graph Embedding （UKGE）， but still have multiple limitations， particularly in modeling complex relations. The UKGE framework can only model simple relation patterns such as symmetry. Although the complex-plane rotation model RotatE is simple and efficient， and can model multi-relation facts by complex rotations， its expressiveness is constrained by the two-dimensional complex space， making it difficult to model high-dimensional rotations， and it is prone to the “gimbal lock” problem， which limits further modeling of complex relations. To address these limitations， an uncertain knowledge graph embedding model based on quaternions， termed QUKGE， was proposed. In QUKGE， entities were represented as four-dimensional quaternion vectors， and relations were modeled as rotation operators in quaternion space. At the scoring function level， quaternion rotation was realized by utilizing the Hamilton product of entity and relation embeddings， thereby representing a variety of complex relation patterns systematically， including symmetry， asymmetry， inverse relations， commutativity， and non-commutativity. The three-dimensional rotation characteristics of quaternions effectively alleviate the “gimbal lock” problem in high-dimensional rotation and significantly enhance the capability to model complex relationships. To validate the effectiveness of QUKGE， five comparative experiments were conducted on three public uncertain knowledge graph datasets： CN15K， NL27K， and PPI5K. Experimental results demonstrate that on the NL27K dataset， QUKGE achieves a 2.9 percentage points improvement in F1 score and a 1.0 percentage point increase in accuracy compared to the MUKGE （Multiplex Uncertain Knowledge Graph Embedding） model on relational fact classification task， providing support for future research in UKGE.