It is constructively proved that the multi-input–multi-output fuzzy systems based upon genuine many-valued implications are universal approximators (they are called Boolean type fuzzy systems in this paper). The general approach to construct such fuzzy systems is given, that is, through the partition of the output region (by the given accuracy). Two examples are provided to demonstrate the way ...

We present an innovative adaptive, model following control scheme and apply it to control a chaotic system with unknown parameters. We illustrate the proposed approach with control of Duffing oscillator problem. The same idea is used to solve three important problems: suppression of chaos, anticontrol of chaos and chaos synchronization. We propose to use ‘approximators’ linearly parameterized b...

The problem of simultaneous approximations of a given function and its derivatives, has been addressed frequently in pure and applied mathematics. In pure mathematics, Bernstein polynomials get their importance from the fact that they provide simultaneous approximation of a function and its derivatives. In neural network theory, feedforward networks were shown to be universal approximators of a...

This paper presents an indirect adaptive system based on neuro-fuzzy approximators for the speed control of induction motors. The uncertainty including parametric variations, the external load disturbance and unmodeled dynamics is estimated and compensated by designing neuro-fuzzy systems. The contribution of this paper is presenting a stability analysis for neuro-fuzzy speed control of inducti...

It is proved that the single input and single output (SISO) fuzzy systems based upon genuine many-valued implications are universal approximators. It is shown theoretically that fuzzy control systems based upon genuine many-valued implications are equivalent to those based upon t-norm implications, the general approach to construct fuzzy systems is given. It is also shown that defuzzi8er based ...

Although, in literature various results can be found claiming that fuzzy controllers are universal approximators, recently it was shown [3, 4] that for Sugeno-controllers this property does not hold any longer if the number of the rules is bounded. Namely, it was shown that the set of Sugeno-controllers is nowhere dense in the space of continuous functions. In this paper a generalization of the...

the present article investigates the application of high order tsk (takagi sugeno kang) fuzzy systems in modeling photo voltaic (pv) cell characteristics. a method has been introduced for training second order tsk fuzzy systems using anfis (artificial neural fuzzy inference system) training method. it is clear that higher order tsk fuzzy systems are more precise approximators while they cover n...

The paper discusses the generalization capability of two hidden layer neural networks based on various fuzzy operators introduced earlier by the authors as Fuzzy Flip-Flop based Neural Networks (FNNs), in comparison with standard networks tansig function based, MATLAB Neural Network Toolbox in the frame of a simple function approximation problem. Various fuzzy neurons, one of them based on new ...

In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system capable of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This resul...

In this paper, we consider a fundamental theoretical question, Why does fuzzy control have such good performance for a wide variety of practical problems?. We try to answer this fundamental question by proving that for each fixed fuzzy logic belonging to a wide class of fuzzy logics, and for each fixed type of membership function belonging to a wide class of membership functions, the fuzzy logi...