An inclusion/exclusion fuzzy hyperbox classifier

Abstract

In this study we consider the classification (supervised learning) problem in [0 1]$^n$ that utilizes fuzzy sets as pattern classes. Each class is described by one or more fuzzy hyperbox defined by their corresponding minimum- and maximum vertices and the hyperbox membership function. Two types of hyperboxes are created: inclusion hyperboxes that contain input patterns belonging to the same class, and exclusion hyperboxes that contain patterns belonging to two or more classes, thus representing contentious areas of the pattern space. With these two types of hyperboxes each class fuzzy set is represented as a union of inclusion hyperboxes of the same class minus a union of exclusion hyperboxes. The subtraction of sets provides for efficient representation of complex topologies of pattern classes without resorting to a large number of small hyperboxes to describe each class. The proposed fuzzy hyperbox classification is compared to the original Min-Max Neural Network and the Gene ral Fuzzy Min-Max Neural Network and the origins of the improved performance of the proposed classification are identified. These are verified on a standard data set from the Machine Learning Repository.