Abstract: The notion of complexity has recently become a serious challenge to scientific research in a multi-disciplinary 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 if-then 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 7-8 show the application of the theoretical results from Sections 4-6 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 Multiple-Input-Multiple-Output 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.