A neural architecture for fuzzy classification with applications

The ability to classify complex patterns is found in biological systems of all degrees of complexity, and designing such pattern classification aspects into synthetic systems has proven to be a difficult yet worthwhile endeavor. Among the challenges encountered in such endeavors is the fact that designed systems which operate within realistic domains must be capable of performing in inherently noisy and uncertain environments. This thesis develops and demonstrates an original approach to automated pattern classification which benefits from the fusion of fuzzy logic and artificial neural networks. This approach represents, propagates, and aggregates uncertainty by implementing fuzzy logic constructs upon an efficient neural architecture. We define a mathematical model which provides a framework for the realization of this pattern classifier, which we call the Fuzzy Voronoi Neurol Network (FVNet). As a neural network-based fuzzy classifier, the FVNet displays a highly parallel architecture which can be trained to adapt to the geometric aspects of a given application. The FVNet training procedure accomplishes classifier adaptation by designing a global network architecture based upon the construction of a Voronoi diagram on points representing typical class feature vectors in multidimensional space. This produces a structured, modular network architecture that is shown to be uniquely flexible. The FVNet is subsequently refined by locally tuning initial class decision surfaces generated during the global architecture design. In addition, the FVNet is distinguished by its use of subnetwork structures within the global architecture to learn fuzzy logic constructs from empirical data.; Because of the expressive nature of fuzzy logic, the FVNet provides classification information beyond the capability of many traditional binary classifiers, including partial and multiple class membership. This requires new methods to accurately measure the classifier's performance. We present a new performance measure, called the modified fuzzy divergence, which is particularly suited to evaluating neuro-fuzzy classifiers. It is based upon the interpretation of information theoretic concepts within a fuzzy logic framework to determine the divergence between the actual and the desired classifier outputs, averaged over a test set. The modified fuzzy divergence is used to evaluate the performance of the FVNet in numerous examples throughout the thesis.