Kernel shapes of fuzzy sets in fuzzy systems for function approximation Export

@article{citeulike:5488519, abstract = {The shapes of if-part fuzzy sets affect the approximating capability of fuzzy systems. In this paper, the fuzzy systems with the kernel-shaped if-part fuzzy sets are built directly from the training data. It is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single-input-single-output (SISO) case. On the basis of these rates, the relationships between the approximating capability and the shapes of if-part fuzzy sets are developed for the fuzzy systems. Furthermore, the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions. The theoretical results are confirmed from the simulation data. In addition, the estimations of the uniform approximation rates are extended to the multi-input-single-output (MISO) case.}, address = {New York, NY, USA}, author = {Luo, Qiang and Yang, Wenqiang and Yi, Dongyun}, citeulike-article-id = {5488519}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1316236}, citeulike-linkout-1 = {http://dx.doi.org/10.1016/j.ins.2007.09.020}, doi = {10.1016/j.ins.2007.09.020}, issn = {0020-0255}, journal = {Inf. Sci.}, keywords = {fuzzy\_logic}, number = {3}, pages = {836--857}, posted-at = {2009-08-19 23:13:06}, priority = {2}, publisher = {Elsevier Science Inc.}, title = {Kernel shapes of fuzzy sets in fuzzy systems for function approximation}, url = {http://dx.doi.org/10.1016/j.ins.2007.09.020}, volume = {178}, year = {2008} }

TY - JOUR ID - citeulike:5488519 L3 - citeulike-article-id:5488519 N2 - The shapes of if-part fuzzy sets affect the approximating capability of fuzzy systems. In this paper, the fuzzy systems with the kernel-shaped if-part fuzzy sets are built directly from the training data. It is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single-input-single-output (SISO) case. On the basis of these rates, the relationships between the approximating capability and the shapes of if-part fuzzy sets are developed for the fuzzy systems. Furthermore, the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions. The theoretical results are confirmed from the simulation data. In addition, the estimations of the uniform approximation rates are extended to the multi-input-single-output (MISO) case. IS - 3 JF - Inf. Sci. SN - 0020-0255 AD - New York, NY, USA EP - 857 TI - Kernel shapes of fuzzy sets in fuzzy systems for function approximation PB - Elsevier Science Inc. VL - 178 SP - 836 KW - fuzzy_logic AU - Luo, Qiang AU - Yang, Wenqiang AU - Yi, Dongyun PY - 2008/// UR - http://dx.doi.org/10.1016/j.ins.2007.09.020 ER -