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...

תיאור מלא

מידע ביבליוגרפי
Main Authors: Fernández Sánchez, Juan, Úbeda Flores, Manuel
פורמט: info:eu-repo/semantics/article
שפה:English
יצא לאור: 2023
נושאים:
גישה מקוונת:https://www.sciencedirect.com/science/article/abs/pii/S0165011423001975
http://hdl.handle.net/10835/14929
תיאור
סיכום: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.