<p>Investigating the informativeness and reducibility of competence models within the framework of fuzzy competence-based knowledge structure theory, this study integrates formal concept analysis with fuzzy set theory by introducing fuzzy skill contexts and defining corresponding disjunctive and conjunctive fuzzy formal concepts, forming two types of fuzzy concept lattices. These lattices serve as structural representations of the relationship between knowledge states and fuzzy competence states. Lattice-theoretic characterizations of informativeness are established: one fuzzy disjunctive (conjunctive) competence model is more informative than another if and only if its corresponding concept lattice is finer in terms of concept intents. Furthermore, the reducibility of fuzzy disjunctive (conjunctive) competence models is investigated, with the existence and uniqueness of irreducible domain restrictions proved. This work extends the classical binary competence models to a fuzzy setting, offering a more realistic and granular representation of partial skill mastery, with potential applications in adaptive learning and educational assessment.</p>