A version of the Stone-Weierstrass theorem in fuzzy analysis

Abstract

Let C ( K , E 1 ) be the space of continuous functions defined between a compact Hausdorff space K and the space of fuzzy numbers E 1 endowed with the supremum metric. We provide a set of sufficient conditions on a subspace of C ( K , E 1 ) in order that it be dense. We also obtain a similar result for interpolating families of C ( K , 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 R n