TY - JOUR
ID - 2823
TI - Universal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Li, Dechao
AU - Xie, Yongjian
AD - School of Mathematics, Physics and Information Science, Zhejiang Ocean
University, Zhoushan, Zhejiang, 316022, China and Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, Zhejiang, 316022,
China
AD - College of Mathematics and Information Science, Shaanxi Normal
University, Xi'an, 710062, China
Y1 - 2016
PY - 2016
VL - 13
IS - 6
SP - 89
EP - 110
KW - Interval-valued fuzzy sets
KW - Interval-valued fuzzy implications
KW - Interval-valued fuzzy systems
KW - Universal approximator
KW - Sufficient condition
DO - 10.22111/ijfs.2016.2823
N2 - It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy. A formula to compute the lower upper bounds on the number of interval-valued fuzzy sets needed to achieve a pre-specified approximation accuracy for an arbitrary multivariate continuousfunction is then presented. In addition, a method to design the interval-valued fuzzy systems based on $R$- and $S$-implications in order to approximate a given continuousfunction with a required approximation accuracy is represented. Finally, two numerical examples are provided to illustrate the proposed procedure.
UR - http://ijfs.usb.ac.ir/article_2823.html
L1 - http://ijfs.usb.ac.ir/article_2823_cce3164c37f2e5e7a4a00262757ae87b.pdf
ER -