Pattern Classification Using Fuzzy Min-Max Neural Network

Abstract

In this thesis we studied two of the most promising neural network classifiers called as fuzzy min-max neural networks for pattern classification which comes under the category of supervised learning and employs fuzzy sets to label pattern classes. These classifiers use fuzzy set hyperboxes to classify the patterns. Each fuzzy set is an aggregation of these hyperboxes. The hyperbox is a n-dimensional box totally characterized by means of its min point, max point and a corresponding membership function. A fuzzy min-max learning algorithm determines the min point and max point of the hyperbox. These classifiers have the ability to learn nonlinear class boundaries, incorporate new classes and refine existing classes without retraining of the entire network in a single pass through the data. The fuzzy set membership eliminates the crispy decision making and introduces a degree of membership which is extremely useful in high level decision making systems.
The first algorithm uses expansion process to include the new classes and refine the existing classes. It uses contraction process to alleviate overlap and containment between different classes. The second algorithm uses a compensatory neuron to eliminate the overlap and containment. It adds an overlap compensatory neuron (OCN) when whenever there is overlap between two different classes and adds a containment compensatory neuron (CCN) when a hyperbox of different class is contained by hyperbox of another class. The final membership value is calculated for each pattern by merging OCN or CCN with the class membership to decide the class of the pattern.
Here we explain architecture of neural network classifiers, their implementation, learning and recall algorithms with several examples to demonstrate the strong abilities of these fuzzy min-max neural network classifiers.