Some properties of the space of fuzzy-valued continuous functions on a compact set

Authors:
Jin-Xuan Fang;Qiong-Yu Xue
Affiliations:
Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, China;Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, China
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

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.