A version of the Stone-Weierstrass theorem in fuzzy analysis


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


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