We introduce FMC-Net, a facial expression recognition (FER) framework that leverages the hierarchical relationship between discrete facial muscle movements, known as Action Units (AUs), and Facial Expressions (FEs) by integrating two complementary constraint layers. This framework couples data-driven learning with psychology-grounded structure. First, a training-time correlation constraint aligns the two tasks within a multi-task network by softly regularizing a target statistical relationship. This can improve sample efficiency and generalization, particularly under limited or biased data. Second, an inference-time fuzzy rule layer maps the networks probabilistic AU predictions to FEs using compact, human-editable from psychological research, yielding transparent, per-decision attributions. An ensemble then combines the model and rule-based pathways and exposes a disagreement-based risk score for human-in-the-loop triage. This two-layer constraint integration addresses the limitations of single-mechanism approaches: training-time constraints shape the learned representations but lack case-wise transparency, while inference-time rules explain decisions but cannot improve the underlying features. Experiments across diverse datasets, including in-the-wild video and cross-dataset evaluation, validate our approach. Constraint-guided training consistently produces models that outperform competitive baselines, while the rule-based pathway can provide transparency and actionable risk signals towards reliable deployment. The proposed methodology is also generalizable to other machine learning tasks with interdependent outputs.