A note on Zadeh's extensions (Q1595203)

A generalization of the well-known extension principle introduced by Zadeh is discussed. While the extension principle deals with the generalization of the mapping \(f: \mathbb{R}^n\to \mathbb{R}^m\) to fuzzy sets, the study shows that if ``\(f\)'' is continuous then \(f: (F(\mathbb{R}^n), D)\to (F(\mathbb{R}^n), D)\) (where \(F(\mathbb{R}^n)\) is \(a\) the space of compact fuzzy sets) is continuous as well with \(D\) being the supremum over Hausdorff distances between the corresponding level sets.