<p>Compared to typical dichotomous skills, fuzzy skills can represent different proficiencies in skills, enabling more accurate ability assessment and learning guidance. However, the outer fringes of knowledge states may be empty, and the fuzzy competence states and knowledge states do not have a strict one-to-one correspondence, which may lead to the inability to make guidance in certain situations. To address this, we introduce a novel fuzzy competence-based approach for personalized adaptive learning guidance, recommending learning paths via outer master fringes of knowledge states and equivalence class representatives of fuzzy competence states. Additionally, we propose a new method to directly compute these fringes and representatives, enhancing computational efficiency. Finally, simulation experiments indicate that the algorithm implementation of the new method has a shorter running time and lower memory usage compared to existing methods.</p>