A note on knowledge structures delineated by fuzzy skill multimaps

Fuzzy skill multimaps can describe individuals' knowledge states from the perspective of latent cognitive abilities. A discriminative knowledge structure is reducing redundant items to vary the test with the aim of lightening the workload for students, and the bi-discriminative knowledge structure is useful for evaluating ‘relative independence’ items or knowledge points. Moreover, it is highly significant to determine the type of fuzzy skill multimap that delineates a discriminative or bi-discriminative knowledge structure. Additionally, we provide a characterization of fuzzy skill multimaps in order to delineate knowledge spaces, learning spaces and simple closure spaces respectively. Furthermore, there are some interesting applications in the meshing of the delineated knowledge structures and the distributed fuzzy skill multimaps. We also give a more precise analysis regarding the separability (resp. bi-separability) on which condition the information collected within a local assessment can reflect an assessment at the global level, and which condition any of the local domains can localize from given global assessment.