Abstract
This thesis addresses the problem of classification with uncertain input data using fuzzy neural networks. Uncertainty in classification is produced, in most cases, by overlapping among classes due to noise in the input data. However, there are many examples of classification problems where the classes overlap naturally. Conventional classifier design requires the model to arrive to a crisp decision by minimising the probability of misclassification. A decision surface is fitted and a certain compromise is reached in order to artificially separate the overlapping classes. This study suggests that a better approach is to design a classifier capable of deciding which class is most representative of an unknown input pattern and also of signalling whether that pattern belongs to an area of overlap between two classes. In this way, uncertain patterns can be isolated and subject to further analysis. This approach is implemented here through a hierarchical fuzzy-neural system (HFNS) that combines backpropagation neural networks (BNNs) and fuzzy logic techniques. The main feature of the HFNS is its ability to identify patterns belonging to more than one class and send them to a second level of processing for a more exhaustive classification. The HFNS is developed after a detailed analysis and an experimental comparison of various proposed fuzzy-neural models. First, the interval backpropagation neural network is investigated. This model allows the use of both linguistic and numerical information to be used as input to the network. The interval BNN proves to be a good alternative to the design of fuzzy systems (FS) when there is a small amount of rules and when numerical data is available. The ability of the HFNS to detect ambiguous patterns is investigated by replacing with fuzzy partitions, the hard partitions used to label the training data. Two new algorithms for fuzzification of labelling data used for training BNNs are proposed. The algorithms precisely represent the degree of similarity of a training pattern to the different class templates involved in a classification problem. BNN trained using the proposed fuzzy labels improve their ability to detect areas of overlapping among the classes as compared with conventional BNN. In a case study, BNNs trained using the proposed algorithm are applied to the detection of atrial fibrillation episodes in records of the MIT-BIH Database with an average classification rate of 87%. The component blocks of the HFNS are trained using a fuzzy neural model which automatically adjusts the learning rate and the slope of the sigmoid function in the backpropagation algorithm. The model is based on fuzzy associative memories. The aim of this integration is to accelerate the training stage of BNN. It is shown that the fuzzy control of the BNN learning rate decreases the number of training interactions required for reaching convergence. In relation to the fuzzy control of the steepness factor of the sigmoid function, no significant effect is found other than the scaling of the learning rate parameter. The HFNS successfully integrates neural networks and fuzzy logic in a new classification system which outperforms conventional methods in the management of uncertainty at different levels. The HFNS is successfully applied to the classification of anomalous electrocardiogram patterns in a selected record of the MIT-BIT ECG Database with classification rates up to 98%.