Revealing the complex relations among emotions is an important fundamental study in cognitive psychology. From the perspective of natural language processing, the key to exploring the relations among emotions lies in the embedded representation of emotional categories. Recently, there has been some interest in obtaining a category representation in the emotion space that can characterize emotion relations. However, the existing methods for emotion category representations have several drawbacks. For example, fixed dimensionality, the dimensionality of the emotion category representation, depends on the selected dataset. In order to obtain better representations for the emotion categories, this study introduces a supervised contrastive learning representation method. In the previous supervised contrastive learning, the similarity between samples depends on the similarity of the annotated labels of the samples. In order to better reflect the complex relations among different emotion categories, the study further proposes a partially similar supervised contrastive learning representation method, which suggests that samples of different emotion categories (e.g., anger and annoyance) may also be partially similar to each other. Finally, the study organizes a series of experiments to verify the ability of the proposed method and the other five benchmark methods in representing the relationship between emotion categories. The experimental results show that the proposed method achieves satisfactory results for the emotion category representations.