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.