Computational Intelligence: Synergies of Fuzzy Logic, Neural Networks and Evolutionary Computing

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Fuzzy Systems and Applications

3.1 Introduction

The fundamental limitation of traditional mathematics, its tools and techniques is that they cannot cope with humanistic or biological systems (Zadeh, 1999). Some examples of such humanistic systems are economic systems, biological systems, social systems, political systems and, more generally, man-made systems of various types. In other words, the conventional quantitative approaches of system analysis and modelling are intrinsically unsuited for dealing with humanistic systems or any system whose complexity is comparable to that of humanistic systems. Thus, to deal with such systems realistically, we need approaches that are not obsessive about precision and rigorous mathematical formalisms. The alternative approach to traditional notions of systems is based on Zadeh's fuzzy sets and linguistic variables, which bear an approximate relation to primary data. Fuzzy systems are those whose inputs and outputs are described by fuzzy variables and fuzzy relations. The seminal ideas of fuzzy systems can be found in the early papers of Zadeh (1968, 1971, 1972, 1973). Since then, fuzzy logic has found applications in system identification (Zadeh, 1994; Espinosa et al., 2005), modelling (Yager and Filev, 1994; Zadeh, 1994; Shin and Xu, 2009), control (Zadeh, 1994; Wang, 1997; Kovacic and Bogdan, 2006), clustering (Hoeppner et al., 1997; Oliveira and Pedrycz, 2007), image processing (Bezdek et al., 1999) and many others. This chapter will ...