Philippine E-Journals

Graphic Representation of Concepts of Mathematics and Clustering with Mahalanobis Distances

Jeng-ming Yih

 

Abstract:

Information of knowledge structures is useful, because it will be helpful for cognition diagnosis so that remedial instruction becomes feasible. The study aimed to provide an integrated method of fuzzy theory as the basis for an individualized concept of structure analysis. The study used the integrated method of fuzzy theory as basis for individualized concept of structure analysis. This integrates Fuzzy Logic Model of Perception (Abbreviation FLMP) and Interpretive Structural Modeling (ISM). A Fuzzy C-Means algorithm based on Mahalanobis distance (Abbreviation 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. Te study uses the best performance of clustering Algorithm FCM-CM in data analysis and interpretation. Each cluster of data can easily describe features of knowledge structures. Te knowledge structures of Mathematics Concepts were constructed to model the features in the pattern recognition completely. This procedure was useful for cognition diagnosis. Te study concludes that the integrated algorithm could improve the assessment methodology of cognition diagnosis and manage the knowledge structures of Mathematics Concepts.