C++ Neural Networks and Fuzzy Logic: Preface

self−organizing

nonadaptive

learning

training

                                           with exemplars

                                           without exemplars

self−organizing

hidden layers

number

              fixed

              variable

sizes

              fixed

              variable

processing

       additive

       multiplicative

hybrid

                 additive and multiplicative

combining other approaches

                              expert systems

                              genetic algorithms

C++ Neural Networks and Fuzzy Logic:Preface

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Hybrid models, as indicated above, could be of the variety of combining neural network approach with expert

system methods or of combining additive and multiplicative processing paradigms.

Decision support systems are amenable to approaches that combine neural networks with expert systems. An

example of a hybrid model that combines different modes of processing by neurons is the Sigma Pi neural

network, wherein one layer of neurons uses summation in aggregation and the next layer of neurons uses

multiplicative processing.

A hidden layer, if only one, in a neural network is a layer of neurons that operates in between the input layer

and the output layer of the network. Neurons in this layer receive inputs from those in the input layer and

supply their outputs as the inputs to the neurons in the output layer. When a hidden layer comes in between

other hidden layers, it receives input and supplies input to the respective hidden layers.

In modeling a network, it is often not easy to determine how many, if any, hidden layers, and of what sizes,

are needed in the model. Some approaches, like genetic algorithms—which are paradigms competing with

neural network approaches in many situations but nevertheless can be cooperative, as here—are at times used

to make a determination on the needed or optimum, as the case may be, numbers of hidden layers and/or the

neurons in those hidden layers. In what follows, we outline one such application.

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C++ Neural Networks and Fuzzy Logic:Preface

Network Modeling

74

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