We consider the space of continuous functions defined between a locally compact Hausdorff space and the space of fuzzy numbers endowed with the level convergence topology. We obtain a Stone-Weierstrass type theorem for such space of functions equipped with the compact open topology.
As a corollary of the above results, we prove that such functions can be approximated by certain fuzzy-number-valued neural networks and sums of fuzzy-number-valued ridge functions.
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