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Fuzzy basis functions, universal approximation, and orthogonal least-squares learning

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2 Author(s)
Wang, L.-X. ; Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA ; Mendel, J.M.

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

Published in:

Neural Networks, IEEE Transactions on  (Volume:3 ,  Issue: 5 )