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The universal approximation capability of fuzzy systems using translations and dilations of one fixed function (called basis function) as their membership functions is discussed. Such types of fuzzy systems are proved to be universal approximators under conditions that the basis function is integrable, with nonvanishing integral, and a.e. continuous. This result enlarges the family of fuzzy systems which can be universal approximators. Two simulation experiments are designed to verify the conclusion.
The universal approximation capability of fuzzy systems using translations and dilations of one fixed function (called basis function) as their membership functions is discussed. These types of fuzzy systems are proved to be universal approximators under conditions that the basis function is integrable, with nonvanishing integral , and ae continuous. This result enlarges the family of fuzzy systems which can be universal approximators. Two simulation experiments are designed to verify the conclusion.