A version of the Stone-Weierstrass theorem in fuzzy analysis
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Authors
Juan J. Font
- Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain.
Delia Sanchis
- Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain.
Manuel Sanchis
- Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain.
Abstract
Let \(C(K,\mathbb{E}^1)\) be the space of continuous functions defined between a compact Hausdorff space \(K\) and the space of fuzzy numbers \(\mathbb{E}^1\) endowed with the supremum metric.
We provide a set of sufficient conditions on a subspace of \(C(K,\mathbb{E}^1)\) in order that it be dense. We also obtain a similar result for interpolating families of \(C(K,\mathbb{E}^1)\).
As a corollary of the above results we prove that certain fuzzy-number-valued neural networks can approximate any continuous fuzzy-number-valued function defined on a compact subspace of \(\mathbb{R}^n\).
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ISRP Style
Juan J. Font, Delia Sanchis, Manuel Sanchis, A version of the Stone-Weierstrass theorem in fuzzy analysis, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 8, 4275--4283
AMA Style
Font Juan J., Sanchis Delia, Sanchis Manuel, A version of the Stone-Weierstrass theorem in fuzzy analysis. J. Nonlinear Sci. Appl. (2017); 10(8):4275--4283
Chicago/Turabian Style
Font, Juan J., Sanchis, Delia, Sanchis, Manuel. "A version of the Stone-Weierstrass theorem in fuzzy analysis." Journal of Nonlinear Sciences and Applications, 10, no. 8 (2017): 4275--4283
Keywords
- Stone-Weierstrass theorem
- fuzzy numbers
- fuzzy-number-valued continuous functions.
MSC
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