Approximation of Convex Fuzzy Sets

被引：0
|
作者：
Noghin, Vladimir [1 ]
机构：
[1] St Petersburg State Univ, 7-9 Univ Skaya Nab, St Petersburg 199034, Russia
来源：
2017 CONSTRUCTIVE NONSMOOTH ANALYSIS AND RELATED TOPICS (DEDICATED TO THE MEMORY OF V.F. DEMYANOV) (CNSA) | 2017年
基金：
俄罗斯基础研究基金会;
关键词：
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we introduce the concepts of fuzzy space, the distances between points and sets of this space. In addition, a concept of a polyhedral fuzzy set, a convex hull, and a fuzzy direction are proposed. It is proved that a polyhedral fuzzy set is a convex hull of a finite number of fuzzy points and directions. In accordance with the main result of this paper any convex closed fuzzy set with a continuous membership function can be approximated with any degree of accuracy by a fuzzy polytop.
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页码：226 / 228
页数：3
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