Fuzzy systems as universal approximators
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Cites background from "Fuzzy systems as universal approxim..."
...Another more tightly defined class of membership functions satisfying this criteria, as pointed out by Wang [56, 57], is the scaled Gaussian membership function: Ai (x) = aiexp[ (x ci ai )2]; (30) Therefore by choosing an appropriate class of membership functions, we can conclude that the ANFIS with simplified fuzzy if-then rules satisfy the four criteria of the Stone-Weierstrass theorem....
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...Another more tightly defined class of membership functions satisfying this criteria, as pointed out by Wang [56, 57], is the scaled Gaussian membership function: Ai (x) = aiexp[ (x ciai )2]; (30) Therefore by choosing an appropriate class of membership functions, we can conclude that the ANFIS with simplified fuzzy if-then rules satisfy the four criteria of the Stone-Weierstrass theorem....
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Cites background from "Fuzzy systems as universal approxim..."
...If property (88) does not hold, then theabove defuzzi cation formula is modi ed accordingly (Wang, 1992) :y = g(') = Ppj=1 yj wj(')Ppj=1 wj(') : (91)A rule basis may be directly built with crisp conclusions, i.e., Bj are ordinary values in (86)....
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...It is also proved that fuzzy models are universal approximators (Wang, 1992), which is not surprising....
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...If (88) does not hold, then the above defuzzification formula is modified accordingly (Wang, 1992): y = g(cp) = Z=l Yjwj(q) ET=1 Wj(q) f (91)...
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...It is also proved that fuzzy models are universalapproximators (Wang, 1992), which is not surprising....
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References
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