title: Embedding of level-continuous fuzzy sets on Banach spaces
abstract: In this paper we present an extension of the Minkowski embedding theorem, showing the existence of an isometric embedding between the classF/sub c/(X) of compact-convex and level-continuous fuzzy sets on a real separable Banach space X and C([0, 1] * B(X*)), the Banach space of real continuous functions defined on the cartesian product between [0, 1] and the unit ball B(X*) in the dual space X*. Also, by using this embedding, we give some applications to the characterization of relatively compact subsets of F/sub c/(X). In particular, an Ascoli-Arzela type theorem is proved and applied to solving the Cauchy problem x(t) = f(t, x(t)), x(t/sub 0/) = x/sub 0/ on F/sub c/(X)
keyphrases: level-continuous fuzzy sets isometric embedding real separable Banach space real continuous functions cartesian product unit ball dual space Ascoli-Arzela type theorem Cauchy problem compact-convex fuzzy sets