Approximation theory of fuzzy systems based upon genuine many-valued implications: SISO cases

Authors:
Yong-Ming Li;Zhong-Ke Shi;Zhi-Hui Li
Affiliations:
Department of Mathematics, Shaanxi Normal University, Xi'an 710062, People's Republic of China and Department of Automatic Control, Northwestern Polytechnical University, Xi'an 710072, People's Re ...;Department of Automatic Control, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China;Department of Mathematics, Shaanxi Normal University, Xi'an 710062, People's Republic of China
Venue:
Fuzzy Sets and Systems - Fuzzy models
Year:
2002

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Abstract

It is proved that the single input and single output (SISO) fuzzy systems based upon genuine many-valued implications are universal approximators. It is shown theoretically that fuzzy control systems based upon genuine many-valued implications are equivalent to those based upon t-norm implications, the general approach to construct fuzzy systems is given. It is also shown that defuzzifier based upon center of areas is not appropriate to the fuzzy systems based upon genuine many-valued implications.