Construct ability indicators of learning Algebra

Concept structure is one important issue of knowledge management as to human knowledge storage. Pathfinder and item response theory are based on graph theory and psychometrics respectively and this integrated method should be feasible to represent concept structures. The purpose of this research is to investigate a series of theoretical and empirical study about integrated fuzzy system for interpretive structural modeling. This method of CAISM integrates Fuzzy Logic Model of Perception (FLMP) and Interpretive Structural Modeling (ISM). The combined algorithm could analyze individualized concepts structure based on the comparisons with concept structure of expert. Besides, the CAISM is applied in the investigation of ability indicators in the concept of Algebra. The individualized concepts structures, degree of master on con-cepts and results of fuzzy clustering will be displayed clearly. Results about fuzzy clustering of Algebra will be helpful for remedial instructions. It shows that lack of concrete examples in general dimensional space will prevent the development of the general theory. Practical of Items and testing for the concept of Algebra will be accomplished. Related information on individualized concepts structures for the concept of Linear Algebra and Algebra, In the same way, results of fuzzy clustering which is based on Mahalanobis distance, on task-takers will be helpful for remedial instructions. The purpose of this study is to investigate an improved Com-mon covariance matrix with the correlation matrix in the objective function Supervised Clustering Algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance.