Implementation of neuro-fuzzy systems through interval mathematics

Neural network performance is dependent on the quality and quantity of training samples presented to the network. In cases where training data is sparse or not fully representative of the range of values possible, incorporation of fuzzy techniques optimizes performance. That is, while neural networks are excellent classifiers, introducing fuzzy techniques allows the classification of imprecise data. The neuro-fuzzy system presented here is a neural network that processes fuzzy numbers. It uses interval mathematics in its implementation. The neuro-fuzzy system uses a standard feedforward network as its basis. The novelty lies in the fact that it processes fuzzy numbers. Specifically, α-cuts of the fuzzy numbers are represented by interval vectors. The backpropagation with momentum learning rule is derived for interval variables. The resulting equations are then employed for training of the system. Thus, the input and output vectors are interval vectors, and the neuronal operations are modified to deal with the interval numbers. Summation of the resultant α-cuts (interval numbers) provide the final fuzzy valued output. Experimental results show that the neuro-fuzzy system´s performance is vastly improved over a standard neural network and other existing methods for speaker-independent speech recognition, an extremely difficult classification problem