Fuzzy logic systems as approximators - where do we stand today?

Summary form only given. Much of the commercial success of fuzzy logic as used in fuzzy logic systems (FLSs) is due to extrinsic properties of the fuzzy logic, namely to the systems with defuzzification. Since the first engineering application pioneered by Mamdani, until now, FLS control systems are mere function approximators and interpolators conveniently and intuitively built using FLSs. The same is true for neuro-fuzzy systems as well. It is thus surprising that not all FLS designers are fully aware of the potential of FLS and that not all engineering textbooks devoted to FLSs start with explaining some basic rules in FLS design as approximators. We overview the basic theory of FLS approximators, show some avenues of design and new methods, indicate some yet unsolved issues, and offer a glimpse to potential applications. A special emphasis is on the interpolation power of fuzzy logic systems provided with output defuzzifiers and the analysis of the interpolation function related to the input membership functions and to the type of the defuzzifier. Further analysis is devoted to the complexity and precision of approximation with fuzzy logic systems.