Yang Shuqun

The Concept Lattices of Q-Matrices

FCA is applied into Q-matrix theory and modifies that Q is Boolean algebra in terms of Boolean addition, Boolean multiplication, and complement operator Tatsuoka 1991 1995. The structure of Item tree Tatsuoka 1995 is denied, and the concept lattices are constructed which is derived from Q matrix.

The judgment method of valid item and its application

Rule space model (RSM) and attribute hierarchy method (AHM) have been research focuses in cognitive diagnosis. Reduced Q-matrix (incidence matrix between attributes and items), which named Qr matrix, plays an important role in RSM and AHM. The column vector of Qr matrix should satisfy an attribute hierarchy, and the vector is called valid item. Studying attribute hierarchy, the judgment method of valid item is proposed. The method is applied to RSM and AHM, and empirical evidence showed that it performed very well.

Notice of Retraction A Stepwise Augment Algorithm for the Construction of Reduced Q-Matrix

Cognitive Diagnosis is more and more important for education and has been a research focus. Tatsuokas Q-matrix theory has been widely used in Cognitive Diagnosis, in which Reduced Q-matrix (Qr matrix) plays an important role. Two methods generate Qr matrix are considered. One is Tatsuokas method, another is augment algorithm. Based on augment algorithm, a stepwise augment algorithm is proposed. Considering the number of valid items, the stepwise augment algorithm is compared with Tatsuokas method and augment algorithm upon running time. Mathematical models with 8 attributes are built for the three algorithms by linear regression analysis.

An augment algorithm based on sufficient formal context

Formal Concept Analysis(FCA) is one of the powerful tools for cognitive science. A concept lattice induced by a context is the core data structure of FCA. A formal context expresses the incidence relation between objects and attributes. It is obvious that the constraint relation between attributes exists. An attribute hierarchy constituted by the attribute relation inevitably restricts the formation of context. Based on an attribute hierarchy, studying the property of the attribute hierarchy, sufficient formal context is defined, the augment algorithm of generating sufficient context is given, and its performance is shown.

The judgment method of valid objects and its application

There is little room for doubt about Formal Concept Analysis (FCA) as a strong tool to be used in many domains, such as cognitive science, etc. Concept lattice is the basic data structure in FCA, and it is induced by contexts. A context is an incidence matrix that shows the relationship between objects and attributes. Attributes often share hierarchical relations which decide the form of objects. Based on attribute hierarchy, valid/invalid object were defined, the judgment method of valid/invalid object was developed on the relation between reachability matrix and valid objects, and valid object was explained from the perspective of graph theory. The judgment algorithm of valid object was proposed. The analysis of the algorithms also showed linear growth with respect to the number of valid objects. Mathematical models with 10 attributes were built for the algorithms by linear regression analysis.