Fuzzy basis on clustering of knowledge structure with cognition diagnosis for algebra learning

The main purpose of this study is to provide an integrated method and algorithm for knowledge structure analysis and cognition diagnosis. Fuzzy clustering and algorithm of graphic structures analysis are combined so that features of knowledge structures of each cluster are clearly displayed. Concept structure analysis (CSA) could provide individualized knowledge structure. CSA algorithm is the major methodology and it is based on fuzzy logic model of perception (FLMP) and interpretive structural modeling (ISM). CSA could display individualized knowledge structure and clearly represent hierarchies and linkage among concepts for each examinee. Furthermore, fuzzy clustering is used to classify examinee based on response pattern of testing data. Therefore, CSA will be more effectively to display features of each cluster. In this study, the author provide the empirical data for concepts of linear algebra from university students. The results show that students of varied cluster own distinct knowledge structures. CSA combined with fuzzy clustering could be very feasible for cognition diagnosis. Based on the findings and results, some suggestions and recommendations for future research are provided.

[1]  Ulrich Bodenhofer,et al.  A Similarity-Based Generalization of Fuzzy Orderings Preserving the Classical Axioms , 2000, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[2]  Kikumi K. Tatsuoka,et al.  Spotting Erroneous Rules of Operation by the Individual Consistency Index. , 1983 .

[3]  Yi Du,et al.  COMPUTERIZED MASTERY TESTING USING FUZZY SET DECISION THEORY , 1993 .

[4]  P. Giordani,et al.  Component Models for Fuzzy Data , 2006 .

[5]  The Hierarchical Structure of Formal Operational Tasks , 1979 .

[6]  John N. Warfield,et al.  Societal Systems: Planning Policy, Complexity , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  S. Chipman,et al.  Cognitively diagnostic assessment , 1995 .

[8]  John N. Warfield,et al.  SOCIETAL SYSTEMS Planning, Policy and Complexity , 1978 .

[9]  L. Hubert,et al.  Inference Procedures for Ordering Theory , 1977 .

[10]  John N. Warfield,et al.  An Introduction to Systems Science , 2006 .

[11]  W H Batchelder,et al.  A measurement-theoretic analysis of the fuzzy logic model of perception. , 1995, Psychological review.

[12]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[13]  Deng-Jyi Chen,et al.  The Design and Implementaiton of a Diagnostic Test System Based on the Enhanced S-P Model , 2005, J. Inf. Sci. Eng..

[14]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[15]  H.-J. Zimmermann Fuzzy set theory , 2010 .

[16]  T. E. Dinero,et al.  An Initial Look at the Validity of Diagnoses Based on Sato's Caution Index , 1985 .

[17]  David J. Krus,et al.  An Ordering-Theoretic Method to Determine Hierarchies Among Items , 1971 .

[18]  Jay Verkuilen,et al.  Fuzzy Set Theory: Applications in the Social Sciences. Series: Quantitative Applications in the Social Sciences , 2006 .

[19]  Kikumi K. Tatsuoka,et al.  Computerized Cognitive Diagnostic Adaptive Testing: Effect on Remedial Instruction as Empirical Validation , 1997 .