Journal article
A survey on universal approximation and its limits in soft computing techniques
International Journal of Approximate Reasoning, Vol.33(2), pp.185-202
2003
Abstract
This paper deals with the approximation behaviour of soft computing techniques. First, we give a survey of the results of universal approximation theorems achieved so far in various soft computing areas, mainly in fuzzy control and neural networks. We point out that these techniques have common approximation behaviour in the sense that an arbitrary function of a certain set of functions (usually the set of continuous function, C) can be approximated with arbitrary accuracy ε on a compact domain. The drawback of these results is that one needs unbounded numbers of “building blocks” (i.e. fuzzy sets or hidden neurons) to achieve the prescribed ε accuracy. If the number of building blocks is restricted, it is proved for some fuzzy systems that the universal approximation property is lost, moreover, the set of controllers with bounded number of rules is nowhere dense in the set of continuous functions. Therefore it is reasonable to make a trade-off between accuracy and the number of the building blocks, by determining the functional relationship between them. We survey this topic by showing the results achieved so far, and its inherent limitations. We point out that approximation rates, or constructive proofs can only be given if some characteristic of smoothness is known about the approximated function.
Details
- Title
- A survey on universal approximation and its limits in soft computing techniques
- Authors/Creators
- D. Tikk (Author/Creator)L.T. Kóczy (Author/Creator)T.D. Gedeon (Author/Creator)
- Publication Details
- International Journal of Approximate Reasoning, Vol.33(2), pp.185-202
- Publisher
- Elsevier Science Inc.
- Identifiers
- 991005544141607891
- Copyright
- © 2003 Elsevier Science Inc.
- Murdoch Affiliation
- School of Information Technology
- Language
- English
- Resource Type
- Journal article
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- Domestic collaboration
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- 4 Electrical Engineering, Electronics & Computer Science
- 4.61 Artificial Intelligence & Machine Learning
- 4.61.493 Neural-Fuzzy Integration
- Web Of Science research areas
- Computer Science, Artificial Intelligence
- ESI research areas
- Computer Science