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Article

Construction of Consistent Fuzzy Competence Spaces and Learning Path Recommendation

1
School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
2
Fujian Provincial Key Laboratory of Data-Intensive Computing, Quanzhou 362000, China
3
Fujian University Laboratory of Intelligent Computing and Information Processing, Quanzhou 362000, China
4
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(10), 768; https://doi.org/10.3390/axioms14100768
Submission received: 1 September 2025 / Revised: 11 October 2025 / Accepted: 13 October 2025 / Published: 16 October 2025

Abstract

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.
Keywords: knowledge space theory (KST); fuzzy competence state (FC-state); fuzzy competence structure; consistent fuzzy competence space (CFCS); outer fringe; learning path recommendation; gradual and effective learning paths knowledge space theory (KST); fuzzy competence state (FC-state); fuzzy competence structure; consistent fuzzy competence space (CFCS); outer fringe; learning path recommendation; gradual and effective learning paths

Share and Cite

MDPI and ACS Style

Wang, R.; Huang, B.; Li, J. Construction of Consistent Fuzzy Competence Spaces and Learning Path Recommendation. Axioms 2025, 14, 768. https://doi.org/10.3390/axioms14100768

AMA Style

Wang R, Huang B, Li J. Construction of Consistent Fuzzy Competence Spaces and Learning Path Recommendation. Axioms. 2025; 14(10):768. https://doi.org/10.3390/axioms14100768

Chicago/Turabian Style

Wang, Ronghai, Baokun Huang, and Jinjin Li. 2025. "Construction of Consistent Fuzzy Competence Spaces and Learning Path Recommendation" Axioms 14, no. 10: 768. https://doi.org/10.3390/axioms14100768

APA Style

Wang, R., Huang, B., & Li, J. (2025). Construction of Consistent Fuzzy Competence Spaces and Learning Path Recommendation. Axioms, 14(10), 768. https://doi.org/10.3390/axioms14100768

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