Fuzzy dynamical modeling of curriculum architecture: A computational pre-audit protocol for temporal reinforcement continuity in engineering education

Ensuring the continuous development of complex graduate attributes is a central mandate of outcomes-based engineering education. While traditional accreditation matrices verify static programmatic coverage, they do not capture the temporal continuity of this competency reinforcement. This study develops an ex-ante computational pre-audit protocol that conceptualizes the intended curriculum as a discrete-time fuzzy dynamical system. The framework mathematically integrates the discrete application of explicitly documented instructional inputs—representing auditable accreditation evidence—with the continuous dissipation of uncompensated support states. To establish a pedagogical foundation, the state propagation distinguishes the structural retention of hierarchical technical knowledge from the accelerated attenuation of context-dependent transversal skills. Structural adequacy is evaluated utilizing an information-based warning index. Application to distinct engineering curriculum architectures reveals a fundamental structural trade-off: the temporal aggregation of specialized technical instruction, although advantageous for immersive disciplinary training, can systematically displace the explicit reinforcement of transversal attributes, generating a quantifiable structural gap defined as a Chronos Trap . Sensitivity analyses demonstrate that the persistent difference between the two trajectories is associated with the topological spacing of exogenous inputs, while the magnitude of degradation and the crossing of the adequacy boundary remain parameter-dependent. The protocol functions as a proactive screening mechanism for identifying temporal vulnerabilities, supporting targeted pedagogical augmentations via embedded micro-assessments without compromising technical depth or exceeding institutional credit constraints, and establishing a computational foundation for iterative, data-driven curriculum quality assurance.