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...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://www.sciencedirect.com/science/article/abs/pii/S0165011423001975 http://hdl.handle.net/10835/14929 |
| _version_ | 1789406554720567296 |
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| author | Fernández Sánchez, Juan Úbeda Flores, Manuel |
| author_facet | Fernández Sánchez, Juan Úbeda Flores, Manuel |
| author_sort | Fernández Sánchez, Juan |
| collection | DSpace |
| description | 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. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-14929 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2023 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-149292023-12-22T12:18:20Z Quasilineability and topological properties of the set of fuzzy numbers Fernández Sánchez, Juan Úbeda Flores, Manuel Cardinality Fuzzy number Quasilineability Sequence of fuzzy numbers Triangular fuzzy number 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. 2023-12-22T12:18:19Z 2023-12-22T12:18:19Z 2023 info:eu-repo/semantics/article 0165-0114 https://www.sciencedirect.com/science/article/abs/pii/S0165011423001975 http://hdl.handle.net/10835/14929 10.1016/j.fss.2023.108562 en Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
| spellingShingle | Cardinality Fuzzy number Quasilineability Sequence of fuzzy numbers Triangular fuzzy number Fernández Sánchez, Juan Úbeda Flores, Manuel Quasilineability and topological properties of the set of fuzzy numbers |
| title | Quasilineability and topological properties of the set of fuzzy numbers |
| title_full | Quasilineability and topological properties of the set of fuzzy numbers |
| title_fullStr | Quasilineability and topological properties of the set of fuzzy numbers |
| title_full_unstemmed | Quasilineability and topological properties of the set of fuzzy numbers |
| title_short | Quasilineability and topological properties of the set of fuzzy numbers |
| title_sort | quasilineability and topological properties of the set of fuzzy numbers |
| topic | Cardinality Fuzzy number Quasilineability Sequence of fuzzy numbers Triangular fuzzy number |
| url | https://www.sciencedirect.com/science/article/abs/pii/S0165011423001975 http://hdl.handle.net/10835/14929 |
| work_keys_str_mv | AT fernandezsanchezjuan quasilineabilityandtopologicalpropertiesofthesetoffuzzynumbers AT ubedafloresmanuel quasilineabilityandtopologicalpropertiesofthesetoffuzzynumbers |