Construction of Consistent Fuzzy Competence Spaces and Learning Path Recommendation

Artificial intelligence is playing an increasingly important role in education. Learning path recommendation is one of the key technologies in artificial intelligence education applications. This paper applies knowledge space theory and fuzzy set theory to study the construction of consistent fuzzy competence spaces and their application to learning path recommendation. With the help of the outer fringe of fuzzy competence states, this paper proves the necessary and sufficient conditions for a fuzzy competence space to be a consistent fuzzy competence space and designs an algorithm for verifying consistent fuzzy competence spaces. It also proposes methods for constructing and reducing consistent fuzzy competence spaces, provides learning path recommendation algorithms from the competence perspective and combined with a disjunctive fuzzy skill mapping, and constructs a bottom-up gradual and effective learning path tree. Simulation experiments are carried out for the construction and reduction in consistent fuzzy competence spaces and for learning path recommendation, and the simulation studies show that the proposed methods achieve significant performance improvement compared with related research and produce a more complete recommendation of gradual and effective learning paths. The research of this paper can provide theoretical foundations and algorithmic references for the development of artificial intelligence education applications such as learning assessment systems and intelligent testing systems.