Constructive approximation of continuous interval- valued functions

Abstract

In this paper we present a Stone-Weierstrass type result in the context of continuous interval-valued functions defined on a compact Hausdorff space. We also provide a Jackson type approximation result involving the modulus of continuity of interval-valued functions based on the gH-difference of intervals. Finally we show how an interval-valued continuous function can be approximated using interval neural networks. All the proofs are constructive.