Papers by Author: Chin Chun Chen

Abstract: Knowledge Management of Mathematics Concepts was essential in educational environment. The purpose of this study is to provide an integrated method of fuzzy theory basis for individualized concept structure analysis. This method 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. Fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-M) was proposed to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. A new improved Fuzzy C-Means algorithm based on a Normalized Mahalanobis distance (FCM-NM) is proposed. Use the best performance of clustering Algorithm FCM-NM in data analysis and interpretation. Each cluster of data can easily describe features of knowledge structures. Manage the knowledge structures of Mathematics Concepts to construct the model of features in the pattern recognition completely. This procedure will also useful for cognition diagnosis. To sum up, this integrated algorithm could improve the assessment methodology of cognition diagnosis and manage the knowledge structures of Mathematics Concepts easily.

Abstract: The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Mahalanobis 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. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Mahalanobis Clustering Algorithm Based on FCM.

Abstract: Currently, cognitive psychologists and mathematics educators are looking again at conceptual and procedural knowledge in mathematics learning. Building relationship between conceptual knowledge and the procedures of mathematics contributes to long-term memory of procedures and to their effective use. So we know that symbols could enhance concept and procedures apply concepts to solve problem efficiently. Sketch the graph of exponential function and logarithmic function. Find the inverse exponential function, logarithmic function and so on. The lack of other concrete example in general exponential and logarithmic function prevented the development of application about general exponential and logarithm. Numerical fundamental mathematic problems are provided with complicated number frequently. The lack of other concrete example in general exponential and logarithmic function prevented the development of application about general exponential and logarithm. Numerical fundamental mathematic problems are provided with complicated number frequently The conceptual knowledge, not mechanical algorithms, need more study and thought to identify. But there is a limitation for students use some materials to clarify complicated mathematic concepts perfectly. In order to insight the misconception of learning fundamental mathematics and progress teaching. The purpose of this study is to provide an integrated method of fuzzy theory basis for individualized concept structure analysis. This method 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. Applying the method of the cluster of fuzzy c-mean, we could distinguish characteristics of six groups. We analysis the whole data and discuss the relationship between knowledge structures of the sample. The result and discoveries from the research can offer pupils' misconception of learning fundamental mathematics with reference of diagnosis.

Abstract: The purpose of this study is to integrate pathfinder and item response theory so as to manage concept structures. 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. Besides, fuzzy clustering technique is adopted to provide features of concept structures based on homogeneity of sample. In this study, the empirical data is the assessment of linear algebra for university students. The important concepts of linear algebra consist of subspace, spanning, linear independent, R² and R³ and many literatures indicate concept structures of linear algebra will influence advanced mathematics. However, little is known about the concept structure and cognition diagnosis on linear algebra. In this study, it shows that lack of concrete examples in general dimensional space will prevent the development of the general theory. There are some limitations for students to use some materials to clarify complicated mathematic concepts perfectly. Most students could not be able to use the geometric insight and apply the Pythagorean of R² or R³. It shows that methodology of the pathfinder and item response theory will reveal important information of concept structures for students. In addition, fuzzy clustering could distinguish characteristics of concept structures on linear algebra. Finally, some limitations and suggestions as to this study are discussed.

Abstract: In this paper, a generalized multivalent fuzzy measure of extensional L-measure, called high order extensional L-measure, is proposed. It is proved that if the value of order index is equal to one, this new measure is just the extensional L-measure, and the larger the value of order index is, the more sensitive it is. A real data set with 5- fold cross-validation MSE is conducted, for comparing the performances of the Choquet integral regression model based on this new measure with other four measures, P-measure and λ-measure, and authors’ two measures, L-measure and extensional L-measure, and two traditional regression model, multiple regression model and ridge regression model, the result show that the Choquet integral regression model based on this new measure has the best performance.

Abstract: Euclidean distance function based fuzzy clustering algorithms can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters by employing Mahalanobis distance in objective function, however, both of them need to add some constrains for Mahalanobis distance. In this paper, the authors’ improved Fuzzy C-Means algorithm based on common Mahalanobis distance (FCM-CM) is used to identify the mastery concepts in linear algebra, for comparing the performances with other four partition algorithms; FCM-M, GG, GK, and FCM. The result shows that FCM-CM has better performance than others.