A novel approach to the derivation of fuzzy membership functions using the Falcon-MART architecture C. Quek * , W.L. Tung Intelligent Systems Laboratory, Nanyang Technological University, School of Computer Engineering, Blk N4, #2a-32 Nanyang Avenue, Singapore 639798, Singapore Received 27 April 2000; received in revised form 7 September 2000 Abstract A fuzzy neural network, Falcon-MART, is proposed in this paper. This is a modi®cation of the original Falcon-ART architecture. Both Falcon-ART and Falcon-MART are fuzzy neural networks that can be used as fuzzy controllers or applied to areas such as forgery detection, pattern recognition and data analysis. They constitute a group of hybrid systems that incorporate fuzzy logic into neural networks. In this way, the structure of these hybrid networks become transparent as high level IF-THEN human-like reasoning is used to interpret the network connections. In addition, the hybrid networks automatically derive the fuzzy rules knowledge base) of the problem domain using neural network techniques and hence avoid the pitfalls of traditional fuzzy systems. The main problem in designing a fuzzy neural network is how to formulate the fuzzy rule base. Most proposed fuzzy neural networks in the literature could be classi®ed into two categories. The ®rst group assumes the existence of a preliminary rule base and uses neural tech- niques to tune the parameters to obtain the ®nal set of fuzzy rules. The second group assumes no knowledge of any fuzzy rules and performs a cluster analysis on the numerical training data before formulating the rules from the computed clusters. Falcon-ART attempts to overcome the constraints faced by these two groups of fuzzy neural networks by using the fuzzy ART technique to partition the training data set. However, there are several shortcomings in the Falcon-ART network. They are: 1. Poor network performances when the classes of input data are closely similar to each other; 2. Weak resistance to noisy/spurious training data; 3. Termination of network training process depends heavily on a preset error parameter; and 4. Learning eciency may deteriorate as a result of using complementary coded training data. Falcon-MART has been developed to address these shortcomings. To evaluate the eectiveness of Falcon-MART, three dierent sets of experiments are conducted. The ®rst experiment demonstrates the eciency of Falcon-MART over Falcon-ART using the Fisher'sIrisdata set. The second experiment evaluates the modeling capability of Falcon-MART againsttheclassicalmulti-layeredperceptronMLP)networkusingasetoftrac¯owdata.Thelastexperimentusesaset of phoneme data to demonstrate the clustering ability of Falcon-MART against the traditional K-nearest-neighbor K-NN) classi®er. The results obtained are encouraging. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Falcon-ART; Falcon-MART; Noisy data; Complementary coding; Fuzzy rules; Classi®cation; Fuzzy neural networks; Adaptive resonance theory www.elsevier.nl/locate/patrec Pattern Recognition Letters 22 2001) 941±958 * Corresponding author. Tel.: +65-790-4926; fax: +65-792-6559. E-mail address: ashcquek@ntu.edu.sg C. Quek). 0167-8655/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII:S0167-865501)00033-2