Abstract

Over the last few decades, fuzzy logic has been shown as a powerful methodology for dealing with imprecision and nonlinearity efficiently. Applications can be found in a wide context ranging from medicine to finance, from human factors to consumer products, from vehicle control to computational linguistics, and so on (Wang 1997; Dubois and Prade 2000; Passino and Yurkovich 1998; Jang et al. 1997; Sugeno 1985; Pedrycz 1993). However, one of the shortcomings of fuzzy logic is the lack of systematic design. To circumvent this problem, fuzzy logic is usually combined with Neural Networks (NNs) by virtue of the learning capability of NNs. NNs are networks of highly interconnected neural computing elements that have the ability of responding to input stimuli and learning to adapt to the environment. Both fuzzy systems and NNs are dynamic and parallel processing systems that estimate input-output functions (Mitra and Hayashi 2000). The merits of both fuzzy and neural systems can be integrated in Fuzzy Neural Networks (FNNs) (Lee and Lee 1974, 1975; Pal and Mitra 1999; Zanchettin and Ludermir 2003). Therefore, the integration of fuzzy and neural systems leads to a symbiotic relationship in which fuzzy systems provide a powerful framework for expert knowledge representation, while NNs provide learning capabilities.

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