Chi-squared-based vs. entropy-based mechanisms for building fuzzy discretizers, inducers and classifiers

This paper proposes an automatic knowledge acquisition system that includes mechanisms for generating fuzzy partitions, inducing fuzzy decision trees and inferring fuzzy classifications. Both discretizer and inducer designing need a dissimilarity measure to choose the appropriate partitions and the most significant predictors among the candidate ones. Although current approaches use the entropy as a measure, our study focuses on adapting a c2 distance in order to accommodate a probabilistic test with a fuzzy data description. Summarizing such data within fuzzy contingency tables provides formal support to apply the c2-test for independence. The advantage of using a c2-based measure instead of an entropy-based one is to control probabilistically the partitioning as well as the splitting mechanisms. However, handling accurately the test procedure in fuzzy context needs restricting the practicable covering schemata for allowing the interpretation of membership degree vectors in terms of probability distributions. Finally, the fuzzy inducer can be employed to build fuzzy classifiers, namely to apply a fuzzy inference mechanism in order to classify new (unseen) cases. Experimental evidence derived from comparative tests confirms that a c2-based inducer produces more accurate and reliable results than an entropy-based one.