A note on Zadeh's extensions

Abstract

Let f : R n → R n and f ̂ : F( R n) → F( R) n be Zadeh's extension of f to the space of fuzzy compact sets F( R n) . The aim of this paper is to show that if f is continuous, then f ̂ : ( F( R n),D) → ( F( R n),D) is also continuous, D being the supremum over Hausdorff distances between their corresponding level sets.