1992/01/01 by L.-X. Wang, Jerry M. Mendel, J.M. Mendel · 4 citations
Computer Science · Engineering · #Advanced Algorithms and Applications #Fuzzy Logic and Control Systems #Neural Networks and Applications
paper · doi:10.1109/72.159070
openalex publication_date 1992/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.