On Contradiction and Inclusion Using Functional Degrees
The notion of inclusion is a cornerstone in set theory and therefore, its generalization in fuzzy set theory is of great interest. The degree of f-inclusion is one generalization of such a notion that differs from others existing in the literature because the degree of inclusion is considered as a m...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2020-04-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125938836/view |
| _version_ | 1811300813818036224 |
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| author | Nicolás Madrid Manuel Ojeda-Aciego |
| author_facet | Nicolás Madrid Manuel Ojeda-Aciego |
| author_sort | Nicolás Madrid |
| collection | DOAJ |
| description | The notion of inclusion is a cornerstone in set theory and therefore, its generalization in fuzzy set theory is of great interest. The degree of f-inclusion is one generalization of such a notion that differs from others existing in the literature because the degree of inclusion is considered as a mapping instead of a value in the unit interval. On the other hand, the degree of f-weak-contradiction was introduced to represent the contradiction between two fuzzy sets via a mapping and its definition has many similarities with the f-degree of inclusion. This suggests the existence of relations between both f-degrees. Specifically, following this line, we analyze the relationship between the f-degree of inclusion and the f-degree of contradiction via the complement of fuzzy sets and Galois connections. |
| first_indexed | 2024-04-13T06:56:56Z |
| format | Article |
| id | doaj.art-65620af409b849f3aee7a515f823cabb |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-13T06:56:56Z |
| publishDate | 2020-04-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-65620af409b849f3aee7a515f823cabb2022-12-22T02:57:13ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832020-04-0113110.2991/ijcis.d.200409.001On Contradiction and Inclusion Using Functional DegreesNicolás MadridManuel Ojeda-AciegoThe notion of inclusion is a cornerstone in set theory and therefore, its generalization in fuzzy set theory is of great interest. The degree of f-inclusion is one generalization of such a notion that differs from others existing in the literature because the degree of inclusion is considered as a mapping instead of a value in the unit interval. On the other hand, the degree of f-weak-contradiction was introduced to represent the contradiction between two fuzzy sets via a mapping and its definition has many similarities with the f-degree of inclusion. This suggests the existence of relations between both f-degrees. Specifically, following this line, we analyze the relationship between the f-degree of inclusion and the f-degree of contradiction via the complement of fuzzy sets and Galois connections.https://www.atlantis-press.com/article/125938836/viewFuzzy setsInclusion measureContradiction measureGalois connections |
| spellingShingle | Nicolás Madrid Manuel Ojeda-Aciego On Contradiction and Inclusion Using Functional Degrees International Journal of Computational Intelligence Systems Fuzzy sets Inclusion measure Contradiction measure Galois connections |
| title | On Contradiction and Inclusion Using Functional Degrees |
| title_full | On Contradiction and Inclusion Using Functional Degrees |
| title_fullStr | On Contradiction and Inclusion Using Functional Degrees |
| title_full_unstemmed | On Contradiction and Inclusion Using Functional Degrees |
| title_short | On Contradiction and Inclusion Using Functional Degrees |
| title_sort | on contradiction and inclusion using functional degrees |
| topic | Fuzzy sets Inclusion measure Contradiction measure Galois connections |
| url | https://www.atlantis-press.com/article/125938836/view |
| work_keys_str_mv | AT nicolasmadrid oncontradictionandinclusionusingfunctionaldegrees AT manuelojedaaciego oncontradictionandinclusionusingfunctionaldegrees |