Universal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications

Document Type : Research Paper


1 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

2 College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China


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 continuous
function 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 continuous
function with a required approximation accuracy is represented. Finally, two numerical examples are provided to illustrate the proposed procedure.


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