A Learning Path Recommendation Approach in a Fuzzy Competence Space

This study proposes a learning path recommendation method based on fuzzy competence space theory. It is developed within the theoretical framework of knowledge space theory and fuzzy set theory, aiming to address the progressive nature of learners’ skill acquisition. The proposed method ensures that a learner can improve their knowledge state by increasing only one proficiency level of a skill at a time, thereby closely reflecting the incremental characteristics of real-world learning processes. Based on fuzzy skill mappings, this work systematically defines fuzzy competence states, fuzzy competence structures, and consistent fuzzy competence spaces. Then, given a consistent fuzzy competence space and a fuzzy skill mapping, the necessary and sufficient conditions for the existence of gradual and effective learning paths are proposed and proven under the disjunctive model. Finally, a gradual and effective learning path recommendation algorithm is designed, and its effectiveness is validated through simulation experiments. This method provides a theoretical foundation and algorithmic support for the development of adaptive learning systems and intelligent testing systems.