Implementation of Nonlinear Fuzzy Models Using Microcontrollers
AFSS '02 Proceedings of the 2002 AFSS International Conference on Fuzzy Systems. Calcutta: Advances in Soft Computing
Sufficient and necessary conditions for Boolean fuzzy systems as universal approximators
Information Sciences: an International Journal
Kernel shapes of fuzzy sets in fuzzy systems for function approximation
Information Sciences: an International Journal
Input-output modelling with decomposed neuro-fuzzy ARX model
Neurocomputing
Some approximation properties of adaptive fuzzy systems with variable universe of discourse
Information Sciences: an International Journal
An evolving-onstruction scheme for fuzzy systems
IEEE Transactions on Fuzzy Systems
Information Sciences: an International Journal
Hi-index | 0.00 |
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 with as minimal system configuration as possible. The general MISO fuzzy systems employ almost arbitrary continuous input fuzzy sets, arbitrary singleton output fuzzy sets, arbitrary fuzzy rules, product fuzzy logic AND, and the generalized defuzzifier containing the popular centroid defuzzifier as a special case. Our necessary conditions are developed under the practically sensible assumption that only a finite set of extrema of the multivariate continuous function to be approximated is available. We have first revealed a decomposition property of the general fuzzy systems: A r-input fuzzy system can always be decomposed to the sum of r simpler fuzzy systems where the first system has only one input variable, the second one two input variables, and the last one r input variables. Utilizing this property, we have derived some necessary conditions for the fuzzy systems to be universal approximators with minimal system configuration. The conditions expose the strength as well as limitation of the fuzzy approximation: (1) only a small number of fuzzy rules may be needed to uniformly approximate multivariate continuous functions that have a complicated formulation but a relatively small number of extrema; and (2) the number of fuzzy rules must be large in order to approximate highly oscillatory continuous functions. A numerical example is given to demonstrate our new results.