7.1 Introduction

Over the past two decades there has been a strong resurgence in the field of data based nonlinear system modelling and identification involving researchers from diverse disciplines. Mathematical equations, or functional mappings, are constructed from observational data from diverse fields, such as electrical engineering, chemical processes, biomedical systems or economic systems. In engineering a class of artificial neural networks (ANN) have been proven to be capable of representing a class of unknown nonlinear input output mappings with arbitrary small approximation error capability ^{[1] , [2]}. The ANN are well structured for adaptive learning, have provable learning and convergence conditions (for at least linear-in-the-parameters networks), and have the capability of parallel processing and good generalisation properties for unseen data. An historically alternative approach is a fuzzy logic (FL) system ^{[3] , [4]} which has found significant practical applications in domestic products, FL controllers, pattern recognition and information processing. The advantage of the FL approach is its logicality and transparency, where it is easy to incorporate a priori knowledge about a system into an explicit fuzzy rule base. Additionally FL represents a form of imprecision and uncertainty common in linguistics through expressions of vagueness. A neuro-fuzzy theory ^{[4] [9]} brings the ideas of ANN and FL together in a cohesive framework, such that the resultant model has a linear-in-the-parameters networks structure for learning properties, and is associated with a fuzzy rule base about the generated data knowledge.

Fuzzy systems ^{[3] ,}