Adaptive Neuro-Fuzzy Systems

One benefit of fuzzy systems (Zadeh, 1965; Ruspini et al., 1998; Cox, 1994) is that the rule base can be created from expert knowledge, used to specify fuzzy sets to partition all variables and a sufficient number of fuzzy rules to describe the input/output relation of the problem at hand. However, a fuzzy system that is constructed by expert knowledge alone will usually not perform as required when it is applied because the expert can be wrong about the location of the fuzzy sets and the number of rules. A manual tuning process must usually be appended to the design stage which results in modifying the membership functions and/or the rule base of the fuzzy system. This tuning process can be very timeconsuming and error-prone. Also, in many applications expert knowledge is only partially available or not at all. It is therefore useful to support the definition of the fuzzy rule base by automatic learning approaches that make use of available data samples. This is possible since, once the components of the fuzzy system is put in a parametric form, the fuzzy inference system becomes a parametric model which can be tuned by a learning procedure. Fuzzy logic and artificial neural networks (Haykin, 1998; Mehrotra et al., 1997) are complementary technologies in the design of intelligent systems. The combination of these two technologies into an integrated system appears to be a promising path toward the development of Intelligent Systems capable of capturing qualities characterizing the human brain. Both neural networks and fuzzy logic are powerful design techniques that have their strengths and weaknesses. Table 1 shows a comparison of the properties of these two technologies (Fuller, 2000). The integrated system will have the advantages of both neural networks (e.g. learning abilities, optimization abilities and connectionist structures) and fuzzy systems (humanlike IF-THEN rules thinking and ease of incorporating expert knowledge) (Brown & Harris,1994). In this way, it is possible to bring the low-level learning and computational power of neural networks into fuzzy systems and also high-level humanlike IF-THEN thinking and reasoning of fuzzy systems into neural networks. Thus, on the neural side, more and more transparency is pursued and obtained either by prestructuring a neural network to improve its performance or by possible interpretation of the weight matrix following the learning stage. On the fuzzy side, the development of methods allowing automatic tuning of the parameters that characterize the fuzzy system can largely draw inspiration from similar methods used in the connectionist community. This combination does not usually mean that a neural network and a fuzzy system are used together in some way.