In this paper, the approximation problem of SISO fuzzy systems by frames is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basis functions (FBF), we first discuss the mathematical theory of frames in a Hilbert space, and then the conditions under which a FBF is a valid frame. Fuzzy membership functions which constitute a valid frame can universally approximate any continuous function. The triangular membership function is demonstrated as such, and it's approximation properties are discussed.
|Number of pages||6|
|State||Published - 1 Jan 1995|
|Event||Proceedings of the 1995 IEEE International Conference on Fuzzy Systems. Part 1 (of 5) - Yokohama, Jpn|
Duration: 20 Mar 1995 → 24 Mar 1995
|Conference||Proceedings of the 1995 IEEE International Conference on Fuzzy Systems. Part 1 (of 5)|
|Period||20/03/95 → 24/03/95|