Abstract
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.
| Original language | English |
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| Pages | 2057-2062 |
| Number of pages | 6 |
| State | Published - 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
| Conference | Proceedings of the 1995 IEEE International Conference on Fuzzy Systems. Part 1 (of 5) |
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| City | Yokohama, Jpn |
| Period | 20/03/95 → 24/03/95 |