Dynamic system approach in sensitivity analysis of neural and fuzzy systems

Martyna Weigl; Witold Kosiński

Martyna Weigl Institute of Fundamental Technological Research Polish Academy of Sciences
Witold Kosiński Polish- Japanese Institute of Information Technology

Abstract

In the paper some results of investigations of two intelligent information systems: a feedforward neural network and an adaptive fuzzy expert system, are presented. The systems can be used for example in approximation and control problems or in diagnostics. The adaptive fuzzy expert system is constructed as a hybrid in which a fuzzy inference system is combined with a neural network. In the learning process for given set of training points an optimal value of the so-called generalized weight vector is searched. The Lapunov theory is used to examine the non-sensitivity of the optimal value of a generalized weight vector to initial conditions and training data. Some necessary and sufficient conditions are formulated in terms of the Hessian matrix of the error function.

Keywords

mapping neural networks, fuzzy inference systems, fuzzy expert systems, training process, optimal value, sensitivity, Lapunov theory, asymptotic stability,

References

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