Fuzzy Type Relations and Transformation Operators Defined by Monads
Using the theory of monads in categories and the theory of monadic relations, the concept of general transformation operator defined by a monadic relation is introduced. It is proven that a number of standard relations used in categories of fuzzy structures are monadic relations for monads defined i...
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| Format: | Article |
| Language: | English |
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Springer
2020-10-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125944869/view |
| _version_ | 1828342347466801152 |
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| author | Jiří Močkoř |
| author_facet | Jiří Močkoř |
| author_sort | Jiří Močkoř |
| collection | DOAJ |
| description | Using the theory of monads in categories and the theory of monadic relations, the concept of general transformation operator defined by a monadic relation is introduced. It is proven that a number of standard relations used in categories of fuzzy structures are monadic relations for monads defined in these categories. It is also proven that a number of standardly used transformation operators in fuzzy sets, fuzzy rough sets, or fuzzy soft sets are in the form of general operators defined by monadic relations. |
| first_indexed | 2024-04-13T23:28:32Z |
| format | Article |
| id | doaj.art-05cd0fd2f4884b6289877006129def3f |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-13T23:28:32Z |
| publishDate | 2020-10-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-05cd0fd2f4884b6289877006129def3f2022-12-22T02:24:59ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832020-10-0113110.2991/ijcis.d.200924.001Fuzzy Type Relations and Transformation Operators Defined by MonadsJiří MočkořUsing the theory of monads in categories and the theory of monadic relations, the concept of general transformation operator defined by a monadic relation is introduced. It is proven that a number of standard relations used in categories of fuzzy structures are monadic relations for monads defined in these categories. It is also proven that a number of standardly used transformation operators in fuzzy sets, fuzzy rough sets, or fuzzy soft sets are in the form of general operators defined by monadic relations.https://www.atlantis-press.com/article/125944869/viewPowerset objectmonadMonadic relationTransformation operator defined by monadic relation |
| spellingShingle | Jiří Močkoř Fuzzy Type Relations and Transformation Operators Defined by Monads International Journal of Computational Intelligence Systems Powerset object monad Monadic relation Transformation operator defined by monadic relation |
| title | Fuzzy Type Relations and Transformation Operators Defined by Monads |
| title_full | Fuzzy Type Relations and Transformation Operators Defined by Monads |
| title_fullStr | Fuzzy Type Relations and Transformation Operators Defined by Monads |
| title_full_unstemmed | Fuzzy Type Relations and Transformation Operators Defined by Monads |
| title_short | Fuzzy Type Relations and Transformation Operators Defined by Monads |
| title_sort | fuzzy type relations and transformation operators defined by monads |
| topic | Powerset object monad Monadic relation Transformation operator defined by monadic relation |
| url | https://www.atlantis-press.com/article/125944869/view |
| work_keys_str_mv | AT jirimockor fuzzytyperelationsandtransformationoperatorsdefinedbymonads |