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In 1991 the idea that the apparatus of Generalized Nets (GNs, see [A1, A2,
A3, A4]) can be used as a mathematical foundation of the Artificial
Intelligence (AI) was introduced (see [A5]). During the last years, a lot of
results were obtained and a lot of papers and books were published connected
to the realization of this idea. Already, there are GN-models describing the
way of functioning and the results of the work of separate types of
databases and expert systems. The separate types of genetic algorithms and
of ant collony optimizations are described by GNs. The processes of pattern
and speech recognition and of scene analysis also are represented by GNs.



Now it is clear that the GNs are not only a tool for modelling of processes,
but a methodology for their description, simulation and (that is the most
import) extension. After describing of the expert system by a GN, there was
shown that the concept of an expert system can be extended with new
components, so that from one side the new expert system also to be modelled
by a GN, and from another hand, the new expert system to have essentially
new components. For example, expert systems with priorities of their facts
and roles were introduced. Expert systems with special meta-facts, that
change the rules, but that are essentially more suitable for applying were
constructed. As extensions of fuzzy expert systems, intuitionistic fuzzy
expert systems were defined. Expert systems that can answer to temporal and
modal questions were described.



In the present book the authors collect a part of their research in the area
of Neural Networks (NNs). Here we construct GNs representing the way of
functioning and the results of the work of separate types of NNs. Here we
describe feedforward types of NNs as multilayer perceptron (MPL) by GNs. Here, we
give also GNs that determine the optimal forms of NNs and MPL using golden 
sections algorithm. The possibility of the parallel work and transfer of information
among a lot of NNs, but in the frames of one GN is discussed.



In the second book we will discuss the program realization of the GN-models,
describing here.

So, we like to show that the apparatus of the GNs is a suitable tool for
modelling of NNs.