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Universal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 13، شماره 6، اسفند 2016، صفحه 89-110 اصل مقاله (403.53 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2823 | ||
| نویسندگان | ||
| Dechao Li* 1؛ Yongjian Xie2 | ||
| 1School 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 | ||
| 2College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Interval-valued fuzzy sets؛ Interval-valued fuzzy implications؛ Interval-valued fuzzy systems؛ Universal approximator؛ Sufficient condition | ||
| مراجع | ||
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