Soft Sets with Atoms
The theory of finitely supported structures is used for dealing with very large sets having a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo-Fraenkel by allowing infinitely many basic elements with no internal structure (atoms) and by equipping classical s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/1956 |
| _version_ | 1827658817185251328 |
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| author | Andrei Alexandru Gabriel Ciobanu |
| author_facet | Andrei Alexandru Gabriel Ciobanu |
| author_sort | Andrei Alexandru |
| collection | DOAJ |
| description | The theory of finitely supported structures is used for dealing with very large sets having a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo-Fraenkel by allowing infinitely many basic elements with no internal structure (atoms) and by equipping classical sets with group actions of the permutation group over these basic elements. On the other hand, soft sets represent a generalization of the fuzzy sets to deal with uncertainty in a parametric manner. In this paper, we study the soft sets in the new framework of finitely supported structures, associating to any crisp set a family of atoms describing it. We prove some finiteness properties for infinite soft sets, some order properties and Tarski-like fixed point results for mappings between soft sets with atoms. |
| first_indexed | 2024-03-09T23:09:58Z |
| format | Article |
| id | doaj.art-99affdb314174d69bfc311082e265046 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:09:58Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-99affdb314174d69bfc311082e2650462023-11-23T17:47:19ZengMDPI AGMathematics2227-73902022-06-011012195610.3390/math10121956Soft Sets with AtomsAndrei Alexandru0Gabriel Ciobanu1Institute of Computer Science, Romanian Academy, 700505 Iaşi, RomaniaFaculty of Computer Science, Alexandru Ioan Cuza University, 700506 Iaşi, RomaniaThe theory of finitely supported structures is used for dealing with very large sets having a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo-Fraenkel by allowing infinitely many basic elements with no internal structure (atoms) and by equipping classical sets with group actions of the permutation group over these basic elements. On the other hand, soft sets represent a generalization of the fuzzy sets to deal with uncertainty in a parametric manner. In this paper, we study the soft sets in the new framework of finitely supported structures, associating to any crisp set a family of atoms describing it. We prove some finiteness properties for infinite soft sets, some order properties and Tarski-like fixed point results for mappings between soft sets with atoms.https://www.mdpi.com/2227-7390/10/12/1956finitely supported setsfinitely supported complete latticessoft setsun-finite setsfixed points |
| spellingShingle | Andrei Alexandru Gabriel Ciobanu Soft Sets with Atoms Mathematics finitely supported sets finitely supported complete lattices soft sets un-finite sets fixed points |
| title | Soft Sets with Atoms |
| title_full | Soft Sets with Atoms |
| title_fullStr | Soft Sets with Atoms |
| title_full_unstemmed | Soft Sets with Atoms |
| title_short | Soft Sets with Atoms |
| title_sort | soft sets with atoms |
| topic | finitely supported sets finitely supported complete lattices soft sets un-finite sets fixed points |
| url | https://www.mdpi.com/2227-7390/10/12/1956 |
| work_keys_str_mv | AT andreialexandru softsetswithatoms AT gabrielciobanu softsetswithatoms |