%0 Journal Article
%T Universal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Li, Dechao
%A Xie, Yongjian
%D 2016
%\ 12/29/2016
%V 13
%N 6
%P 89-110
%! Universal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications
%K Interval-valued fuzzy sets
%K Interval-valued fuzzy implications
%K Interval-valued fuzzy systems
%K Universal approximator
%K Sufficient condition
%R 10.22111/ijfs.2016.2823
%X 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.
%U http://ijfs.usb.ac.ir/article_2823_cce3164c37f2e5e7a4a00262757ae87b.pdf