Competence-based fuzzy skill functions

Fuzzy skill functions connect knowledge states at the performance level with latent cognitive abilities at the competence level. Given that there may exist precedence relations among skills, the main idea of this study is trying to develop fuzzy competence structures restricted on the fuzzy sets of skills that are likely to occur. We consider the knowledge structures determined by fuzzy skill functions and fuzzy competence structures. More precisely, disjunctive fuzzy skill functions delineate knowledge spaces if the fuzzy competence structures are union-closed, while conjunctive fuzzy skill functions delineate simple closure spaces if the fuzzy competence structures are intersection-closed. In general, competence-based fuzzy skill function delineates knowledge structures depending on the effective competence states. Correspondingly, we build algorithms that delineate knowledge structures via competence-based fuzzy skill functions. In the courses of these algorithms, one does not need to list all fuzzy competence states of fuzzy competence structures.