Gegov A. Fuzzy Networks for Complex Systems. A Modular Rule Base Approach

Springer, 2010. — 298 p.This book introduces the novel concept of a fuzzy network. In particular, it describes further developments of some results from its predecessor book on Complexity Management in Fuzzy Systems, published in 2007 in the Springer Series in Studies in Fuzziness and Soft Computing.
The book contents build on a number of special presentations made by the author at international scientific events in the recent years. These presentations include an invited lecture at the EPSRC International Summer School in Complexity Science in 2007, tutorials at the IEEE International Conferences on Fuzzy Systems in 2007 and 2010, tutorials at the IEEE International Conferences on Intelligent Systems in 2008 and 2010, a tutorial at the IFSA World Congress in 2009 as well as plenary lectures at the WSEAS International Conferences on Fuzzy Systems in 2008 and Artificial Intelligence in 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, the understanding of 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 elements within this entity. The qualitative aspect is often characterised by uncertainty about data, information or knowledge that relates to 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 elements of an entity and the connections reflect the interactions among these elements. In this case, the scale of the entity is reflected by the overall size of the network whereas the number of elements is given by the number of nodes.
An obvious way of dealing with qualitative complexity is to use the concept of a fuzzy network. The latter consists of nodes and connections whereby the nodes are fuzzy systems and the connections reflect the interactions among these fuzzy systems. In this case, the uncertainty about data, information or knowledge related to an entity are reflected by the rule bases of the corresponding fuzzy systems and the underlying fuzzy logic.
In the context of the considerations made above, a fuzzy network represents a natural counterpart of a neural network. Both neural networks and fuzzy networks are computational intelligence based networks with nodes and connections. However, the nodes in a neural network are represented by neurons whereas the nodes in a fuzzy network are represented by rule bases.Types of Fuzzy Systems
Formal Models for Fuzzy Networks
Basic Operations in Fuzzy Networks
Structural Properties of Basic Operations
Advanced Operations in Fuzzy Networks
Feedforward Fuzzy Networks
Feedback Fuzzy Networks
Evaluation of Fuzzy Networks