概率逻辑与模糊逻辑在精细化学习诊断中的对比研究

精细化学习诊断有助于客观准确探究学生学习现状，为实施有针对性的补救教学提供理论和数据支持。本文对比研究概率逻辑与模糊逻辑在精细化学习诊断中的表现。首先，从“概念”视角介绍和对比两种逻辑。其次，介绍两个分别基于上述两逻辑的代表性模型：HO-PINC和Fuzzy-DINA。然后，对比两模型在五个实证数据上表现。最后，通过模拟研究进一步对比两模型的心理计量学性能。DIC等模型-数据拟合指标和RMSE等参数返真性指标的结果表明两模型对同一批数据有较一致的分析结果。建议实践者忽略模型选择对数据分析的影响，从概念或思辨视角入手选择使用概率逻辑或模糊逻辑来定义属性。

A Comparative Study of Probabilistic Logic and Fuzzy Logic in Refined Learning Diagnosis

Learning diagnosis can be regarded as the application of cognitive diagnosis in learning assessment. Currently, most conventional learning diagnosis models (LDM) are constructed based on binary attributes, and the diagnosis results show that students’ knowledge of each attribute can be classified into two categories: mastery and non-mastery. However, this dichotomy is too crude to satisfy the refined assessment of student’s learning statue and thus cannot realize the fine distinction of individual differences between different students. Therefore, the development of LDM with refined learning diagnosis function is a topic of both theoretical and practical significanceCurrently, there are two kinds of refined LDMs, i.e., the probabilistic LDMs and the fuzzy LDMs, which are respectively based on probabilistic logic and fuzzy logic. However, currently, no studies have compared these two models, which bring difficulties to practitioners in model selection. To this end, this study compares and analyzes the application effects of probabilistic logic and fuzzy logic in refined learning diagnosis from four perspectives: concept, model function, empirical data analysis, and simulation study.Firstly, probability logic and fuzzy logic are introduced and compared from the perspective of concept. Essentially, fuzzy logic is a type of deterministic uncertainty and probability logic is a type of uncertain determinacy. They focus on two different kinds of uncertainties in the same event, one is the uncertainty of event occurrence, and another one is the event ambiguity (i.e., to what degree it occurs).Secondly, two representative LDMs based on probability logic and Fuzzy logic are introduced: the HO-PINC model and the Fuzzy-DINA model. The item response functions of them are quite similar. And the main difference between them is that the probability or degree of ideal correct response of person n to item i is defined in different ways, i.e., for the HO-PINC model and for the Fuzzy-DINA model, where δ and t is the probabilistic attribute and the fuzzy attribute, respectively.Thirdly, the performance of these two models in five empirical data is compared. The results indicated that, compared with the HO-PINC model, the Fuzzy-DINA model can not only provide consistent estimates of model parameters, but also has a slightly better model-data relative fitting.Finally, a simple simulation study based on Q-matrices of varying degrees of complexity was conducted to further compare the performance of these two models. The results showed that, regardless of the Q-matrix, the parameter estimation results of these two models have a quite high correlation, which is basically consistent with the empirical research results.Overall, the results show that the psychometric performance of these two models are basically identical, but the Fuzzy-DINA model has a few advantages in model-data fitting than the HO-PINC model. However, this study is only a shallow study on the performance of probabilistic logic and fuzzy logic in refined learning diagnosis, and there are some limitations in the study itself, which cannot fully explain the superiority of probabilistic logic and fuzzy logic.