Abstract:
In this paper, the approximation problem of SISO fuzzy systems is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basi...Show MoreMetadata
Abstract:
In this paper, the approximation problem of SISO fuzzy systems is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basic functions (FBF's), we first give a systematic and detailed analysis of FBF's and present five properties of FBF's: structure similarity and compatibility between the membership functions and FBF's, complementarity and less fuzziness of FBF's, and composition of fuzzy systems. These properties provide a clear picture of the shape and features of FBF's. Based on these properties of FBF's, we obtain some basic approximation properties of fuzzy systems: basic approximation property, uniform approximation property, uniform convergent property and universal approximation property. These results reveal the basic approximation mechanism of fuzzy systems and verify a few basic ideas in the design of fuzzy systems.<>
Published in: IEEE Transactions on Fuzzy Systems ( Volume: 2, Issue: 2, May 1994)
DOI: 10.1109/91.277964
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Approximation Theory ,
- Mechanistic Basis ,
- Properties Of Systems ,
- Basic Properties ,
- Problem Of Systems ,
- Estimation Problem ,
- Membership Function ,
- Fuzzy Set ,
- Fuzzy System ,
- Fuzzy Function ,
- Universal Property ,
- Uniform Properties ,
- Single-input Single-output ,
- Approximation Properties ,
- Value Function ,
- Universe ,
- Input Variables ,
- Rule-based ,
- Systemic Factors ,
- Input Space ,
- Fuzzy Rules ,
- Universal Type ,
- Fuzzy Logic ,
- Output Space ,
- Fuzzy Control ,
- Multi-input Multi-output
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Approximation Theory ,
- Mechanistic Basis ,
- Properties Of Systems ,
- Basic Properties ,
- Problem Of Systems ,
- Estimation Problem ,
- Membership Function ,
- Fuzzy Set ,
- Fuzzy System ,
- Fuzzy Function ,
- Universal Property ,
- Uniform Properties ,
- Single-input Single-output ,
- Approximation Properties ,
- Value Function ,
- Universe ,
- Input Variables ,
- Rule-based ,
- Systemic Factors ,
- Input Space ,
- Fuzzy Rules ,
- Universal Type ,
- Fuzzy Logic ,
- Output Space ,
- Fuzzy Control ,
- Multi-input Multi-output
