Fuzzy Logic on Representation of Knowledge Structure and Measure of Similarity with Application on Mathematics Concepts for Pupils

Abstract

The purpose of this study is to investigate the knowledge structure representation based on fuzzy theory. With response data and item-concept matrix, the psychometric model item response theory (IRT) is used to calibrate latent trait and fuzzy logic model of perception (FLMP) is to calculate individualized fuzzy subordinate matrix among concepts. Similarity measurement of fuzzy basis on the subordinate matrix provides the comparisons between knowledge structures of each student and the expert. Fuzzy structural modeling (FSM) is used to construct the individualized knowledge structures which display hierarchies and relationship among concepts. A testing data set on axiom concepts for pupils is analyzed and it displays three groups according to fuzzy c-means on similarity values of each student. Each group displays its specific characteristics of knowledge structure. The integrated methodology on similarity measurement and representation of individualized knowledge structure analysis could provide helpful information for remedial instruction.