Plenary Lecture
Complex Systems Modelling by Rule Based Networks
Professor Alexander Gegov
University of Portsmouth
School of Computing, Buckingham Building
Portsmouth PO1 3HE
United Kingdom
Email: alexander.gegov@port.ac.uk
Abstract: The notion of complexity has recently become a serious
challenge to scientific research in a multidisciplinary context. For example,
it is quite common to find complex systems in biology, cosmology, engineering,
computing, finance and other areas. However, building models for complex
systems is often a difficult task.
There are two main aspects of complexity – quantitative and qualitative. The
quantitative aspect is usually associated with a large scale of an entity or a
large number of units within this entity. The qualitative aspect is often
characterised by uncertainty in the knowledge about an entity.
A natural way of coping with quantitative complexity is to use the concept of
a general network. The latter consists of nodes and connections, whereby the
nodes represent the units within an entity and the connections reflect the
interactions among these units. In this case, the scale of the entity is
reflected by the overall size of the network, whereas the number of units is
given by the number of nodes.
An obvious way of dealing with qualitative complexity is to use the concept of
a rule based network. The latter consists of nodes and connections, whereby
the nodes are rule based systems and the connections reflect the interactions
among these rule based systems. In this case, the uncertainty in the knowledge
about an entity is reflected by the underlying rules.
The lecture consists of ten sections. The first section discusses complexity
as a systemic feature and the ability of rule based systems to handle
different attributes of complexity. Section 2 reviews several types of rule
based systems in the context of systemic complexity, including systems with
single, multiple and networked rule bases. Section 3 introduces the novel
concept of rule based networks by means of formal models such as ifthen rules
and integer tables, Boolean matrices and binary relations, grid and
interconnections structures, incidence and adjacency matrices, and block
schemes and topological expressions. Section 4 presents basic operations on
nodes in rule based networks, including merging and splitting in horizontal,
vertical and output context. Section 5 describes some structural properties of
node operations in rule based networks such as associativity of merging and
variability of splitting in horizontal, vertical and output context. Section 6
illustrates some advanced operations on nodes in rule based networks,
including node transformation for input augmentation, output permutation and
feedback equivalence as well as node identification in horizontal, vertical
and output merging. Sections 78 show the application of the theoretical
results from Sections 46 in feedforward rule based networks with single or
multiple levels and layers as well as in feedback fuzzy networks with single
or multiple local and global feedback. Section 9 gives an overall evaluation
of rule based networks in relation to rule based systems within the Matlab
software environment using fuzzy rules. The last section highlights the
theoretical significance, the application areas and the methodological impact
of rule based networks in the context of a general evaluation of the lecture
contents.
Brief biography of the speaker:
Alexander Gegov is Senior Lecturer in the School of Computing at the
University of Portsmouth. He holds a PhD in Control Systems and a DSc in
Intelligent Systems – both from the Bulgarian Academy of Sciences. His
research interests are in the theory of computational intelligence and complex
systems as well as their application for modelling, simulation and control in
areas such as transport networks and the environment. He has published his
main research results in complex systems in a number of international journals
such as the International Journal of Control and Systems & Control Letters. He
is also the sole author of two books – the first one in the Kluwer Series in
Intelligent Technologies in 1996 and the second one in the Springer Series in
Fuzziness and Soft Computing in 2007. He has been reviewing papers for a
number of journals in computational intelligence such as IEEE Transactions on
Fuzzy Systems and the International Journal of Fuzzy Sets and Systems as well
as research proposals to the Australian Research Council. He was first prize
winner for young researchers of the Bulgarian Union of Scientists in 1996,
invited lecturer to the NATO Advanced Study Institute on Soft Computing in
1997, guest researcher for the EU Project on Fuzzy Algorithms for
MultipleInputMultipleOutput Systems and invited presenter at the UK House
of Commons Conference on Promoting Young Researchers in 2000. He was also
tutorial presenter at the IEEE International Conference on Fuzzy Systems in
2007, invited lecturer at the EPSRC International Summer School in Complexity
Science in 2007, plenary speaker at the WSEAS International Conference on
Fuzzy Systems in 2008 and tutorial presenter at the IEEE International
Conference on Intelligent Systems in 2008. He is a member of and the UK Higher
Education Academy, the International Federation of Automatic Control, the
European Society for Fuzzy Logic and Technology and the European Association
for Promotion of Science and Technology.
