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Fuzzy skill multimaps can describe individuals' knowledge states from theperspective of latent cognitive abilities. The significance of discriminativeknowledge structure is reducing repeated testing and the workload for students,which responds to the so-called `double reduction policy'. As an application inknowledge assessment, the bi-discriminative knowledge structure is useful forevaluating `relative independence' items or knowledge points. Moreover, it isof great significance that which kind of fuzzy skill multimap delineates adiscriminative or bi-discriminative knowledge structure. Moreover, we give acharacterization of fuzzy skill multimaps such that the delineated knowledgestructures are knowledge spaces, learning spaces and simple closure spacesrespectively. Further, there are some interesting applications in the meshingof the delineated knowledge structures and the distributed fuzzy skillmultimaps. We also give a more precise analysis with regard to the separability(resp. bi-separability) on which condition the information collected within alocal assessment can reflect an assessment at the global level, and whichcondition any of the local domains can localize from given global assessment.

A note on knowledge structures delineated by fuzzy skill multimaps