Quasilineability and topological properties of the set of fuzzy numbers

被引：4

作者：

Fernandez-Sanchez, Juan ^{[1
,2
]}

Ubeda-Flores, Manuel ^{[3
]}

机构：

[1] Univ Almeria, Res Grp Theory Copulas & Applicat, Almeria 04120, Spain

[2] Univ Complutense Madrid, Interdisciplinary Math Inst, Madrid 28040, Spain

[3] Univ Almeria, Dept Math, Almeria 04120, Spain

来源：

FUZZY SETS AND SYSTEMS | 2023年 / 465卷

关键词：

Cardinality; Fuzzy number; Quasilineability; Sequence of fuzzy numbers; Triangular fuzzy number; SEQUENCES;

D O I：

10.1016/j.fss.2023.108562

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we show that the cardinality of the set of fuzzy numbers coincides with that of the real numbers. We also show that the set of triangular fuzzy numbers is nowhere dense within the set of fuzzy numbers (with a suitable distance) and that the set of real numbers is also nowhere dense within the set of triangular fuzzy numbers. In addition, we introduce the concept of quasilineability and study the set of bounded fuzzy number sequences that do not have a lower limit and that of monotonic decreasing, bounded with respect a partial ordering and not convergent. & COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：12

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