Abstract:
In this paper, the approximation properties of MIMO fuzzy systems generated by the product inference are discussed. We first give an analysis of fuzzy basic functions (FB...Show MoreMetadata
Abstract:
In this paper, the approximation properties of MIMO fuzzy systems generated by the product inference are discussed. We first give an analysis of fuzzy basic functions (FBF's) and present several properties of FBF's. Based on these properties of FBF's, we obtain several basic approximation properties of fuzzy systems: 1) basic approximation property which reveals the basic approximation mechanism of fuzzy systems; 2) uniform approximation bounds which give the uniform approximation bounds between the desired (control or decision) functions and fuzzy systems; 3) uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions; and 4) universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect. The similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds.<>
Published in: IEEE Transactions on Fuzzy Systems ( Volume: 3, Issue: 2, May 1995)
DOI: 10.1109/91.388175
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- IEEE Keywords
- Index Terms
- Systems Engineering ,
- Fuzzy System ,
- Proof Of Case ,
- Xiamen University ,
- Approximation Theory ,
- Accurate Estimation ,
- Properties Of Systems ,
- Basic Properties ,
- Membership Function ,
- Input Space ,
- Uniform Approximation ,
- Universal Property ,
- Uniform Properties ,
- Universal Approximation ,
- Approximation Properties ,
- Mathematical Approximation ,
- Rule-based ,
- Results Of This Paper ,
- Systemic Factors ,
- Fuzzy Logic ,
- Fuzzy Set ,
- Conditions Of Theorem ,
- Fuzzy Control ,
- Universal Type ,
- Magnitude Of Weights ,
- Intuitive Idea ,
- Assumptions Of Theorem ,
- Piecewise Linear Function ,
- Single-input Single-output ,
- Fuzzy Rules ,
- Fuzzy Numbers ,
- Mathematical Theory
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Systems Engineering ,
- Fuzzy System ,
- Proof Of Case ,
- Xiamen University ,
- Approximation Theory ,
- Accurate Estimation ,
- Properties Of Systems ,
- Basic Properties ,
- Membership Function ,
- Input Space ,
- Uniform Approximation ,
- Universal Property ,
- Uniform Properties ,
- Universal Approximation ,
- Approximation Properties ,
- Mathematical Approximation ,
- Rule-based ,
- Results Of This Paper ,
- Systemic Factors ,
- Fuzzy Logic ,
- Fuzzy Set ,
- Conditions Of Theorem ,
- Fuzzy Control ,
- Universal Type ,
- Magnitude Of Weights ,
- Intuitive Idea ,
- Assumptions Of Theorem ,
- Piecewise Linear Function ,
- Single-input Single-output ,
- Fuzzy Rules ,
- Fuzzy Numbers ,
- Mathematical Theory
