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Fuzzy basis functions, universal approximation, and orthogonal least-squares learning
Abstract
Fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions. Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy. Based on the fuzzy basis function representations, an orthogonal least-squares (OLS) learning algorithm is developed for designing fuzzy systems based on given input-output pairs; then, the OLS algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system. The fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system, and the simulation results show that the control performance is improved by incorporating some common-sense fuzzy control rules.
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Cites
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Cited by
Fuzzy logic systems for engineering: a tutorial
Mendel, J. M. (1995) · Proceedings of the IEEE · doi:10.1109/5.364485 · Cited by 2,110
Self-citationAdaptive Fuzzy Practical Fixed-Time Tracking Control of Nonlinear Systems
Chen, M., Wang, H., & Liu, X. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2019.2959972 · Cited by 405
Yang, Y., Feng, G., & Ren, J. (2004) · IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans · doi:10.1109/tsmca.2004.824870 · Cited by 396
Bounemeur, A., Chemachema, M., & Essounbouli, N. (2018) · ISA Transactions · doi:10.1016/j.isatra.2018.04.014 · Cited by 394
The 2017 IEEE International Conference on Fuzzy Systems
(2016) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2016.2545826 · Cited by 308
Metadata
- Authors
- Wang, L.-X., & Mendel, J. M.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 1992
- Volume
- 3
- Issue
- 5
- Pages
- 807-814
- ISSN
- 1045-9227 (ISSN-L)
- OpenAlex
- W2101036899
- Cited by
- 2,796
- References
- 2
- FWCI
- 33.53
- Type
- journal article
- Language
- en
- Open access
- closed
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- Wang, L.-X., & Mendel, J. M. (1992). Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Transactions on Neural Networks. https://doi.org/10.1109/72.159070
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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