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

被引：18
|
作者：
Fang, Jin-Xuan [1 ]
Xue, Qiong-Yu [1 ]
机构：
[1] Nanjing Normal Univ, Dept Math, Nanjing 210097, Jiangsu, Peoples R China
来源：
FUZZY SETS AND SYSTEMS | 2009年 / 160卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Fuzzy number space; Fuzzy-valued continuous function; Completeness; Compactness; NUMBER SPACE; EMBEDDING PROBLEM; LEVEL CONVERGENCE; TOPOLOGY; SEQUENCE; SUPREMUM; SUBSETS; INFIMUM;
D O I：
10.1016/j.fss.2008.07.014
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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.
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页码：1620 / 1631
页数：12
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