A version of the StoneWeierstrass theorem in fuzzy analysis

Let C(K,E^1) be the space of continuous functions defined between a compact Hausdorff space K and the space of fuzzy numbers E1 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.