Though traditional neural networks and fuzzy logic are powerful universal approximators, however without some refinements, they may not, in general, be good approximators for adaptive systems. By extending fuzzy sets to qualitative fuzzy sets, fuzzy logic may become universal approximators for adaptive systems. Similar considerations can be extended to neural networks.

Both Takagi–Sugeno (TS) and Mamdani fuzzy systems are known to be universal approximators. In this paper, we investigate whether one type of the fuzzy approximators is more economical than the other type. The TS fuzzy systems in this study are the typical two-input single-output TS fuzzy systems: they employ trapezoidal or triangular input fuzzy sets, arbitrary fuzzy rules with linear rule cons...

We prove that three independent fuzzy systems can uniformly approximate Bayesian posterior probability density functions by approximating the prior and likelihood probability densities as well as the hyperprior probability densities that underly the priors. This triply fuzzy function approximation extends the recent theorem for uniformly approximating the posterior density by approximating just...

Wang and Mendel proved (1991) that fuzzy systems with product inference, cen-troid defuzziication, and everywhere positive membership functions (in particular, Gaus-sians, Wang, 1992) are capable of approximating any real continuous control function on a compact set to arbitrary accuracy. Kosko (1992) proved that fuzzy systems, in which membership functions have compact support, and combination...

One of the reasons why fuzzy methodology is successful is that fuzzy systems are universal approximators, i.e., that we can approximate an arbitrary continuous function within any given accuracy by a fuzzy system. In some practical applications (e.g., in control), it is desirable to approximate not only the original function, but also its derivatives (so that, e.g., a fuzzy control approximatin...

Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators wi...

This paper focuses on hardware implementations of fuzzy inference systems which provide low silicon cost, high operational speed and adaptability to different application domains. The architecture and basic building blocks of two fuzzy logic controllers are described and their functionality is illustrated with experimental results showing the capability of these systems to be applied as functio...