Research On Formal Concept Analysis Based On Attribute Hierarchy And Its Application In Cognitive Diagnosis

Formal Concept Analysis (FCA) is proved to be a useful tool for cognitive science. Context expresses an incidence relation of objects with respect to attributes. Prerequisite relationship among attributes decides the constructing of context. So FCA based on attribute hierarchy (AH-FCA) is a meaningful topic. With the development of education reform, cognitive diagnosis has become an increasing important research topic. CAT with cognitive diagnosis (CD-CAT) will benefit computerized testing. It is indicated that specifying attribute hierarchy is necessary before testing. So AH-FCA will hasten CD-CAT, and the concept lattices based on AH-FCA may be ideal cognitive diagnosis models.After introducing FCA, cognitive diagnosis and CAT, based on attribute hierarchy, this dissertation discusses how to generate contexts, and the concept lattices from the contexts are regarded as cognitive diagnosis models. The main contributions of thisdissertation are summarized as follows:(1) The judgment method of valid/invalid item is proposed.The concept of valid/invald item is proposed. The judging of valid/invald item is transferred to simple algebraic operations.(2) Augment algorithm and incremental augment algorithm are proposed for reduced Q -matrix.Considering the judging method of valid/invalid items, augment algorithm and incremental augment algorithm are proposed. The basic ideal is looking for a set of valid items like basis in linear space, and the other valid can be represented linearly by the"basis". So the other items can be obtained augmentally. The basic ideal of incremental augment algorithm is the same as that of augment algorithm. The difference is that augment algorithm is backward augment from reachability matrix, and incremental augment algorithm is forward augment from empty matrix.(3) The algorithm of constructing of concept lattices based on attribute hierarchy is proposed.Godin's algorithm is a classical algorithm in constructing concept lattices. It is found that Godin's algorithm is wrong if Ea -matrix is context, and then the modification of Godin's algorithm is given. Analying Ea -matrix's characteristics, the relationship between Ea -matrix and the concept lattice from the Ea -matrix, the algorithm of constructing concept lattices based on Ea -matrix is proposed. It is empirically show the algorithm performs better than the Godin's algorithm. Combining the incremental augment algorithm, the algorithm of construting concept lattices based on Ea -matrix is extended to that of based on attribute hierarchy.(4) The Theory about CD-CAT based on FCA and Its application.Three basic structures of attribute hierarchy are rationally constructed based on AHM. The concept lattices from attribute hierarchies are served as the models of cognitive diagnosis in CD-CAT. The technology of item bank construction, Item Selection Strategies in CD-CAT and Estimation Method are considered to design an initiatory and systemic CD-CAT. The result of Monte Carlo study shows that examinees'knowledge states are well diagnosed and the precision in examinees'abilities estimation is satisfied.(5) Gradual CD-CAT models based FCA are proposedGranularity affects testing efficiency and diagnosis precision. Considering testing efficiency and diagnosis precision, gradual CD-CAT based on FCA is proposed. Two gradual CD-CAT models are given: one is based on attribute hierarchy, another is based on item space.