An efficient approach for reduction of membership functions and rules in fuzzy systems

When fuzzy inferencing systems are generated automatically using a large amount of training data, they tend to produce a significant number of fuzzy membership functions and rules. This paper shows a new and efficient tree search method of reducing the number of membership functions and removing any duplicate rules produced thereby. Our method views the data as trees rather than tables and hence helps to speed up the process of eliminating duplication. The time complexity of our approach depends on the data and how much it matches, rather than simply the size of the tables. We compare the performance of our tree search method with a linear search technique using different data including real data from a neuro-fuzzy multi-classifier handwritten character recognition system. We show that the time improvement achieved over a linear search method using both synthetic and real data is substantial.