Gradual Sets: An Approach to Fuzzy Sets
In the fuzzy theory of sets and groups, the use of α-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α-levels, it is possible to establish a one to one correspondence which makes possible doubly, a gradual and a functorial treatment of the fuzzy theory....
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2023/6163672 |
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| _version_ | 1832546643862355968 |
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| author | Josefa M. García Pascual Jara |
| author_facet | Josefa M. García Pascual Jara |
| author_sort | Josefa M. García |
| collection | DOAJ |
| description | In the fuzzy theory of sets and groups, the use of α-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α-levels, it is possible to establish a one to one correspondence which makes possible doubly, a gradual and a functorial treatment of the fuzzy theory. The main result of this paper is to identify the class of fuzzy sets, respectively, fuzzy groups, with subcategories of the functorial categories Set (0, 1], resp., Gr (0, 1]. In this line, the algebraic potential of this theory will be reached, in forthcoming papers. |
| format | Article |
| id | doaj-art-0a19fa49297d470e899af0c3ececf2cb |
| institution | Kabale University |
| issn | 1687-711X |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-0a19fa49297d470e899af0c3ececf2cb2025-02-03T06:47:30ZengWileyAdvances in Fuzzy Systems1687-711X2023-01-01202310.1155/2023/6163672Gradual Sets: An Approach to Fuzzy SetsJosefa M. García0Pascual Jara1Department of Applied MathematicsDepartment of Algebra and IMAG (Instituto de Matemáticas)In the fuzzy theory of sets and groups, the use of α-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α-levels, it is possible to establish a one to one correspondence which makes possible doubly, a gradual and a functorial treatment of the fuzzy theory. The main result of this paper is to identify the class of fuzzy sets, respectively, fuzzy groups, with subcategories of the functorial categories Set (0, 1], resp., Gr (0, 1]. In this line, the algebraic potential of this theory will be reached, in forthcoming papers.http://dx.doi.org/10.1155/2023/6163672 |
| spellingShingle | Josefa M. García Pascual Jara Gradual Sets: An Approach to Fuzzy Sets Advances in Fuzzy Systems |
| title | Gradual Sets: An Approach to Fuzzy Sets |
| title_full | Gradual Sets: An Approach to Fuzzy Sets |
| title_fullStr | Gradual Sets: An Approach to Fuzzy Sets |
| title_full_unstemmed | Gradual Sets: An Approach to Fuzzy Sets |
| title_short | Gradual Sets: An Approach to Fuzzy Sets |
| title_sort | gradual sets an approach to fuzzy sets |
| url | http://dx.doi.org/10.1155/2023/6163672 |
| work_keys_str_mv | AT josefamgarcia gradualsetsanapproachtofuzzysets AT pascualjara gradualsetsanapproachtofuzzysets |