Reduction of a Set of Fuzzy Classifiers by Equivalence Classes

The induction of classifiers by means of supervised learning techniques is one of the most common and extended applications in the field of the intelligent systems. Multi-classifier systems obtain a set of basic classifiers and uses it to predict the class of a data instance. In this work, a new method to reduce a set of classifiers to their equivalent minimal set is presented. For this purpose, a new fuzzy classifier called Atomic Fuzzy Classifier is defined. Furthermore, two different definitions of similarity, structural similarity and functional similarity, are considered. The combination of both produces a novel definition of a similarity function between two classifiers. This relation of similarity is used to obtain classes of equivalence, where each element of this class represents a subset of similar classifiers. The original set of classifiers is reduced to a new set of classifiers where only one of them is related to an unique equivalence class. In the experimental part, an application for the classification of elements of the IRIS database is presented.