Convergence of fuzzy sets with respect to the supremum metric

被引：6
|
作者：
Pedraza, Tatiana [1 ]
Rodriguez-Lopez, Jesus [1 ]
Romaguera, Salvador [1 ]
机构：
[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain
来源：
FUZZY SETS AND SYSTEMS | 2014年 / 245卷
关键词：
Supremum metric; Fuzzy set; Gamma-convergence; Hausdorff metric; RELATIVELY COMPACT-SETS; MAPPINGS; SPACE;
D O I：
10.1016/j.fss.2014.03.005
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the alpha-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasi-pseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also provide some results about the behavior of the convergence in the supremum metric with respect to maximizers. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：83 / 100
页数：18
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