A note on knowledge structures delineated by fuzzy skill multimaps

TL;DR

This paper explores how fuzzy skill multimaps can define various knowledge structures, aiding in efficient knowledge assessment and reducing testing workload, with theoretical characterizations and practical applications.

Contribution

It provides a characterization of fuzzy skill multimaps that delineate different knowledge structures and analyzes conditions for local assessments to reflect global knowledge.

Findings

Characterization of fuzzy skill multimaps for knowledge spaces and learning spaces

Conditions for local assessments to reflect global knowledge

Applications in reducing testing workload and knowledge evaluation

Abstract

Fuzzy skill multimaps can describe individuals' knowledge states from the perspective of latent cognitive abilities. The significance of discriminative knowledge structure is reducing repeated testing and the workload for students, which responds to the so-called `double reduction policy'. As an application in knowledge assessment, the bi-discriminative knowledge structure is useful for evaluating `relative independence' items or knowledge points. Moreover, it is of great significance that which kind of fuzzy skill multimap delineates a discriminative or bi-discriminative knowledge structure. Moreover, we give a characterization of fuzzy skill multimaps such that the delineated knowledge structures are knowledge spaces, learning spaces and simple closure spaces respectively. Further, 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 with regard to 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.