Plenary lecture 5: complex systems modelling by rule based networks
Authors: Alexander Gegov
Venue: Proceedings of the 8th WSEAS international conference on Artificial intelligence, knowledge engineering and data bases (2009)

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.