<p>The incorporation of side information, also known as prior knowledge, into the clustering process is a key feature of semi-supervised clustering methods. This incorporation serves to enhance the accuracy of the resulting clusters and facilitates the identification of complex data structures. In practical applications, the relationship between objects and classes is often ambiguous. In order to address the ambiguity inherent in side information and to enhance the accuracy of clustering, this paper proposes a semi-supervised evidential c-means clustering method based on a kernel function. First, the kernel function is employed to map all data into a high-dimensional space, thereby enabling the construction of the objective function of the evidential c-means. To address the imprecise nature of class labels, a penalty term is incorporated into the objective function. The optimal credal partition is identified by the optimization algorithm as a result of clustering. The experimental results demonstrate that the proposed method can effectively reduce execution time while maintaining accuracy.</p>