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32







                                                                            Neural Networks

                                                                         and Fuzzy Systems






                                                              32.1  Neural Networks and Fuzzy Systems
                                                              32.2  Neuron Cell
                                                              32.3  Feedforward Neural Networks
                                                              32.4  Learning Algorithms for Neural Networks
                                                                    Hebbian Learning Rule  •  Correlation Learning
                                                                    Rule  •  Instar Learning Rule  •  Winner Takes All
                                                                    (WTA)  •  Outstar Learning Rule  •  Widrow–Hoff LMS
                                                                    Learning Rule  •  Linear Regression  •  Delta Learning
                                                                    Rule  •  Error Backpropagation Learning
                                                              32.5  Special Feedforward Networks
                                                                    Functional Link Network  •  Feedforward Version of the
                                                                    Counterpropagation Network  •  WTA
                                                                    Architecture  •  Cascade Correlation Architecture  •  Radial
                                                                    Basis Function Networks
                                                              32.6  Recurrent Neural Networks
                                                                    Hopfield Network  •  Autoassociative
                                                                    Memory  •  Bidirectional Associative Memories (BAM)
                                                              32.7  Fuzzy Systems
                                                                    Fuzzification  •  Rule Evaluation  •  Defuzzification  •  Design
                                                                    Example
                                                              32.8  Genetic Algorithms
                                 Bogdan M. Wilamowski               Coding and Initialization  •  Selection and Reproduction  •
                                 University of Wyoming              Reproduction  •  Mutation



                                 32.1 Neural Networks and Fuzzy Systems

                                 New and better electronic devices have inspired researchers to build intelligent machines operating in a
                                 fashion similar to the human nervous system. Fascination with this goal started when McCulloch and
                                 Pitts (1943) developed their model of an elementary computing neuron and when Hebb (1949) intro-
                                 duced his learning rules. A decade later Rosenblatt (1958) introduced the perceptron concept. In the early
                                 1960s Widrow and Holf (1960, 1962) developed intelligent systems such as ADALINE and MADALINE.
                                 Nillson (1965) in his book Learning Machines summarized many developments of that time. The pub-
                                 lication of the Mynsky and Paper (1969) book, with some discouraging results, stopped for some time the
                                 fascination with artificial neural networks, and achievements in the mathematical foundation of the back-
                                 propagation algorithm by Werbos (1974) went unnoticed. The current rapid growth in the area of neural
                                 networks started with the Hopfield (1982, 1984) recurrent network, Kohonen (1982) unsupervised training
                                 algorithms, and a description of the backpropagation algorithm by Rumelhart et al. (1986).





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