Some properties of the space of fuzzy-valued continuous functions on a compact set
In this paper, a generalized form of the Bolzano theorem in classical analysis to fuzzy number space and a characterization of compact subsets in fuzzy number space are given, Some properties of the fuzzy-valued continuous functions defined on a compact set K are studied. Completeness of the space C(K. E(1)) of fuzzy-valued continuous functions on K endowed with the supremum metric D is proved. A characterization of compact subsets in the space (C(K. E(1)), D) is presented, which is a generalization of the Arzela-Ascoli theorem in classical analysis. (C) 2008 Published by Elsevier B.V.
fuzzy-valued continuous function compactness fuzzy number space completeness