HIERARCHICAL NEURO-FUZZY MODELS / MODELOS NEURO-FUZZY HIERÁRQUICOS

FLAVIO JOAQUIM DE SOUZA

This dissertation presents a new proposal of neurofuzzy systems (models), which present, in addition to the learning capacity (which are common to the neural networks and neurofuzzy systems) the following features: learning of the structure; the use of recursive partitioning; a greater number of inputs than usually allowed in neurofuzzy systems; and hierarchical rules. The structure´s definition is needed when implementing a certain model. In the neural network case, for example, one must, first of all, estabilish its structure (number of layers and number of neurons per layers) before any test is performed. So, an important feature for any model is the existence of an automatic learning method for creating its structure. A system that allows a larger number of inputs is also important, in order to extend the range of possible applications. The hierarchical rules feature results from the structure learning method developed for these two models. The work has involved three main parts: study of the existing neurofuzzy systems and of the most commom methods to adjust its parameters; definition and implementation of two hierarchical neurofuzzy models; and case studies. The study of neurofuzzy systems (NFS) was accomplished by creating a survey on this area, including advantages, drawbacks and the main features of NFS. A taxonomy about NFS was then proposed, taking into account the neural and fuzzy features of the existing systems. This study pointed out the limitations of neurofuzzy systems, mainly their poor capability of creating its own structure and the reduced number of allowed inputs. The study of the methods for parameter adjustment has focused on the following algorithms: Least Square estimator (LSE) and its solutions by numerical iterative methods; and the basic gradient descent method and its offsprings such as Backpropagation and Rprop (Resilient Backpropagation). The definition of two new neurofuzzy models was accomplished by considering desirable features and limitations of the existing NFS. It was observed that the partitioning formats and rule basis of the NFS have great influence on its performance and limitations. Thus, the decision to use a new partitioning method to remove or reduce the existing limitations - the recursive partitioning. The Quadtree and BSP partitioning were then adopted, generating the so called Quadree Hierarchical Neurofuzzy model (NFHQ) and the BSP hierarchical Neurofuzzy model (NFHB). By using these kind os partitioning a new class of NFS was obtained allowing the learning of the structure in addition to parameter learning. This Feature represents a great differential in relation to the traditional NFS, besides overcoming the limitation in the number of allowed inputs. In the case studies, the two neurofuzzy models were tested in 16 differents cases, such as traditional benchmarks and problems with a greater number of inputs. Among the cases studied are: the IRIS DATA set; the two spirals problem; the forecasting of Mackey-Glass chaotic time series; some diagnosis and classifications problems, found in papers about machine learning; and a real application involving load forecasting. The implementation of the two new neurofuzzy models was carried out using a 32 bit Pascal compiler for PC microcomputers using DOS or Linux operating system. The tests have shown that: these new models are able to adjust well any data sets; they create its own struture; they adjust its parameters, presenting a good generalization performance; and automatically extract the fuzzy rules. Beyond that, applications with a greater number of inputs for these neurofuzzy models. In short two neurofuzzy models were developed with the capability of structure learning, in addition to parameter learning. Moreover, these new models have good interpretability through hierarchical fuzzy rules. They are not black coxes as the neural networks.

HIERARCHICAL NEURO-FUZZY MODELS / MODELOS NEURO-FUZZY HIERÁRQUICOS

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