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In 1991 the idea that the apparatus of Generalized Nets (GNs, see [A1, 7
A3, A4]) can be used as a mathematical foundation of the Artificial
Intelligence (AI) was introduced (see [8]). 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. There are GNs describing  the processes of machine learning and of decision making, of intellectual games functioning, etc
(see, e.g., [12,16,A6,A7,A8,A9,A10,A11,A12]). 

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. Also, we
describe feedforward types of NNs as multilayer perceptron (MPL) by GNs. Here, we
give 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.

The first attempts to represent NNs by GNs were done 15-20 years ago (see [A13,A14,A15,A16,A17]), but the systematic research started in the joint research of the authors. Here and in another book, we will collect all our research devoted to NNs and GNs. In the second book, that we plan to prepare in a near time, we will discuss the program realization of the GN-models, described here.

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


References

[A1] Alexieva, J., E. Choy, E. Koycheva. Review and bibliography
on generalized nets theory and applications. -- In: A Survey of Generalized Nets
(E. Choy, M. Krawczak, A. Shannon and E. Szmidt, Eds.), Raffles KvB Monograph
No 10, 2007, 207-301.
[A3] Atanassov, K. On Generalized Nets Theory,
   ``Prof. M. Drinov" Academic Publishing House, Sofia, 2007.
[A4] Radeva, V., M. Krawczak, E. Choy.
Review and bibliography on generalized nets theory and applications. 
Advanced Studies in Contemporary Mathematics, Vol. 4, 2002, No 2, 173-199.
[A6] Kolev, B., E. El-Darzi, E. Sotirova, I. Petronias, K. Atanassov, P. Chountas, V. Kodogianis. Generalized Nets in Artificial Intelligence. Vol. 3: Generalized nets, Relational Data Bases and Expert Systems. "Prof. M. Drinov" Academic Publishing House, Sofia, 2006.
[A7] Chountas, P., B. Kolev, E. Rogova, V. Tasseva, K. Atanassov. Generalized Nets in Artificial Intelligence. Vol. 4: Generalized Nets, Uncertain Data and Knowledge Engineering. "Prof. M. Drinov" Academic Publishing House, Sofia, 2007.
[A8] Atanassov, K., G. Gluhchev, S. Hadjitodorov, J. Kacprzyk, A. Shannon, E. Szmidt, V. Vssilev. Generalized Nets Decision Making and Pattern Recognition. Warsaw School of  Information Technology, Warszawa, 2006.
[A9] Shannon, A., D. Langova-Orozova, E. Sotirova, I. Petrounias, K. Atanassov, M. Krawczak, P. Melo-Pinto, T. Kim. Generalized Net Modelling of University Processes. KvB Visual  Concepts Pty Ltd, Monograph No. 7, Sydney, 2005.
[A10] Shannon A., Atanassov K., Orozova D., Krawczak M., Sotirova E., Melo-Pinto P., Petrounias I., Kim T. Generalized nets and information flow within a university. Warsaw School of Information Technology, Warsaw, 2007.
[A11] Atanassov, K., G. Pasi and R. Yager. Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. International Journal of Systems Science, Vol. 36, 2005, No. 14, 859-868.
[A12] Fidanova, S., K. Atanassov. Generalized net models for the process of hybrid ant colony optimization. Comptes Rendus de l'Academie bulgare des Sciences, Tome 61, 2008, No. 12, 1535-1540.



[A13] Hadjyisky L., Atanassov K., Theorem for representation of the neuronal networks by generalized nets. AMSE Review, Vol. 12, No. 3, 1990, 47-54.
[A14] Hadjyisky L., Atanassov K., A generalized net, representing the elements of one neuron network set. AMSE Review, Vol. 14, No. 4, 1990, 55-59. 
[A15] Hadjyisky L., Atanassov K., Generalized nets representing the elements of neuron networks, in Applications of generalized nets, (K. Atanassov, Ed.), World Scientific Publ. Co., Singapore, 1993, 49-67. 
[A16] Hadjyisky L., Atanassov K., 	Generalized net model of the intuitionistic fuzzy neural networks, Advances in Modelling & Analysis, AMSE Press, Vol. 23, 1995, No. 2, 59-64. 
[A17] Kuncheva L., Atanassov K., An intuitionistic fuzzy RBF network, Proceedings of EUFIT'96, Aachen, Sept. 2-5, 1996, 777-781.