In this paper, we propose a formal approach for integrating linguistic fuzzy neural units (LFNUs) with hedge algebra. Hedge algebra provides a systematic method for handling linguistic terms with hedges, allowing for nuanced fuzzy relationships. We formally define the theoretical framework, model architecture, and algorithms for LFNUs based on hedge algebra. The proposed model is implemented and evaluated through experiments, demonstrating its effectiveness in terms of accuracy and interpretability. Our results highlight the potential of LFNUs in enhancing fuzzy neural networks with hedge algebra.