A characterization of relatively compact sets of fuzzy sets

被引：6
作者：
Greco, GH [1 ]
机构：
[1] Univ Trent, Dipartimento Matemat, I-38050 Trento, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2006年 / 64卷 / 03期
关键词：
fuzzy set; compact set; compactness criterion; variational convergence; supremum metric; F-convergence; D-convergence; Hausdorff distance; Kuratowski limit; levelwise convergence; sendograph convergence;
D O I：
10.1016/j.na.2005.03.113
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A purely topological characterization of relatively compact sets is given for the metric space (K(Y), D) of upper semicontinuous, compact-supported, normal fuzzy subsets of a metric space Y. The considered metric D is that of the distance between fuzzy subsets, which is the supremum of the Hausdorff distances of the corresponding level sets. In the given proof the compactness of a variational convergence which was introduced by De Giorgi and Franzoni is fundamental. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码：518 / 529
页数：12
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