Synthesis of probabilistic fuzzy classifiers using GK clustering and Bayesian estimation

Abstract

The paper presents an automatic rule-base design of probabilistic fuzzy systems developed for classification tasks. The objective here is to present a methodology that allows the user to obtain a fuzzy classifier directly from training data, in which rules' antecedents are defined on the basis of clustering techniques and probabilistic consequents allow the presence of all classes in the same individual rule, each class associated with a measure of probability. The probability measure is calculated based on Bayes' theorem using an ideal region of the rule to update a priori information. The clustering process which supports the automatic partition of the input universe is based on the Gustafson-Kessel algorithm and is associated with a principal component analysis to reduce the dimensionality of the input data, improving this way the interpretability of the resulting classifier. The proposed approach is applied to Wine, Wisconsin breast cancer, Sonar e Ionosphere data sets. Results are compared with those of two other classifiers and show that the proposed approach can be an alternative to automatically set antecedents and consequents of probabilistic fuzzy classifiers.