| Research on deriving classifiers has experienced a recent surge due to the importance of data mining applications. Many interesting methods, including neural nets and decision trees, have been developed. Fuzzy systems do not appear to have been thoroughly investigated for this application. Fuzzy systems have an advantage over neural networks in ease of implementation and speed of computation. This dissertation includes an analysis of how to compare classifiers objectively using leave-one-out testing and the linear discriminant, and how to evaluate a classifier's accuracy on a particular data set with an upper bound from the Bayes Rule. It reports research in modifying standard fuzzy systems to apply to classification problems. Although their accuracy is comparable to many of the newer classification methods, standard fuzzy systems are not scalable to high dimensions on data sets of moderate size. The basic Fuzzy Classification Procedure (FCP) overcomes this limitation and is comparable to the linear discriminant on three medical data sets. For one of the medical data sets, it is superior to any of the twenty-two algorithms tested by the StatLog project, but it is inferior to the linear discriminant on the non-medical data sets. Two more complicated algorithms to improve the Basic FCP succeed on the most difficult data set, but do not raise its accuracy for the other data sets. Multivariate approximation algorithms were analyzed and one was shown equivalent to a fuzzy system. This algorithm, originally due to Shepard, was modified for classification problems. It was more accurate on two of the data sets than any other procedure reported in the literature. Finally, an analysis is reported of the computational complexity of the fuzzy classification procedures. |
