2005, Volume 7, Issue 8
Strategic Study of CAE >> 2005, Volume 7, Issue 8
Approximating Characteristics of Fuzzy Systems With Arbitrary Membership Function
1. School of Electrical and Automation Engineering, Tianjing University, Tianjin 300072, China
2. Shandong Provincial Architectural Design & Research Institute Introduction, Jinan 250001, China
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Abstract
While quadrilateral membership function is used as general membership function, Stone-Weierstrass theorem is utilized to prove that fuzzy systems with arbitrary membership functions are capable of approximating any continuous function on a compact set. It is a generalization for theory of basic fuzzy systems approximating any continuous non-linear function. The performance of fuzzy systems to approximate random non-linear function is the theoretical basis of fuzzy system's application in system identification.
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