Skills and fuzzy knowledge structures

In knowledge space theory (KST), knowledge structure is an effective feature to evaluate individuals’ knowledge and guide future learning. How to construct knowledge structures is one of the key research problems in KST. At present, the knowledge structure has been generalized to the polytomous knowledge structure. This article mainly focuses on the special polytomous knowledge structures delineated by Skills, which are called fuzzy knowledge structures. We consider how to construct fuzzy knowledge structures based on the relationship between items and skills, and how to find the learning paths for specific knowledge domains. First, we construct knowledge structures in four models, which are the conjunctive model of skill maps, the disjunctive and conjunctive models of fuzzy skill maps, and the competency model of fuzzy skill multimaps. Second, we assess individuals’ skills and find the learning paths for the specific knowledge domains in the first three models. Finding the learning paths for a specific knowledge domain can guide learning and improve the learning efficiency of individuals. Finally, we analyze some data sets to show that the algorithms proposed are effective and applicable. These works can be applied to adaptive learning systems, which bring great convenience for assessing individuals’ knowledge and guiding future learning.