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Item response theory with fuzzy markup language for parameter estimation and validation

Owing to advanced technical progress in information and communication technology, computerized adaptive assessment becomes more and more important for the personalized learning achievement. According to the response data from the conventional test and three-parameter logistic (3PL) model of the item response theory (IRT), this paper combines IRT with fuzzy markup language (FML) for an adaptive assessment application. The novel FML-based IRT estimation mechanism includes a Gauss-Seidel (GS) parameter estimation mechanism, a fuzzy knowledge base and a fuzzy rule base, to estimate the item parameters for each item. Meanwhile, it is able to infer the possibility of correct response to each item for each involved student. Additionally, this paper also proposes a static-IRT test assembly mechanism to assemble a form for the conventional test. After that, this paper chooses 5-fold cross validation to validate the research performance. From the experimental results, it shows that the proposed approach performs better than the traditional Bayesian estimation one.