Quasilineability and topological properties of the set of fuzzy numbers

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 wit...

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Bibliographic Details
Published in:Fuzzy sets and systems 2023-08, Vol.465, p.108562, Article 108562
Main Authors: Fernández-Sánchez, Juan, Úbeda-Flores, Manuel
Format: Article
Language:English
Subjects:
Cardinality
Fuzzy number
Quasilineability
Sequence of fuzzy numbers
Triangular fuzzy number
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Summary: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.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2023.108562