Tag-based recommendation systems leverage user-generated tags to personalize content filtering, but integrating this data effectively remains challenging due to complex relationships in the user-item-tag space. Existing approaches often overlook triadic relationships among users, items, and tags, limiting the potential of tag-based recommendations. To address these issues, a novel framework incorporating energy distance measures was proposed to model interactions in tag-based RS. This framework introduces an energy-based tag model capturing non-linear relationships through an incompatibility matrix, integrating tag semantics and user behavior modeling. Evaluation on the Movielens 20M dataset showed significant improvement in recommendation accuracy compared to traditional methods, highlighting the capability of energy distance to capture complex tag-based relationships. The study emphasizes the importance of modeling energy-based relationships in utilizing tag information for more effective recommendations, offering theoretical insights and practical implications for personalized system development.