Survey of Fuzzy Approximations

• Main Authors: Liang, Howard, 梁浩鍠
• Other Authors: Yung-Yaw Chen
• Format: Others
• Language: en_US
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/12978005819559366207

碩士 === 國立臺灣大學 === 電機工程學系 === 86 === Abstract This thesis gives a survey about the current development in fuzzy approximations. The most important distinction between the classical approximations and fuzzy approximations is that the fuzzy approximations are one kind of model-free approximation theory. The form, structure or formula of approximated functions is not needed to be known and to be used in the approximation. All the information used in approximation is the input-output pairs of the functions to be approximated. Beside this, there is one unique feature belonging to fuzzy approximations. That is the ability of incorporation of not only numerical information but also linguistic information about the approximated functions. This ability makes the fuzzy approximations can use non-numerical information to help and accelerate the approximation. In this thesis, the main focus is devoted to the survey of universal fuzzy approximation sets developed. It gives a clear list of this kind of approximation sets and their reference papers for the sake of in-depth study. The other focus is the rule extraction methods developed recently. General nonlinear black-box modeling techniques are mentioned. Various approximation properties of fuzzy systems are also collected and well documented in this thesis. As a result of the survey, a clear picture of the recent state of fuzzy approximations will be obtained.