Quasi-Copulas, Copulas and Fuzzy Implicators
In this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas. We show that there is a one-to-one correspondence between the classes of all quasi-copulas and 1-Lipschitz fuzzy implicators. A similar relation holds for copula...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2020-06-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125941266/view |
| _version_ | 1811300783095808000 |
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| author | Radko Mesiar Anna Kolesárová |
| author_facet | Radko Mesiar Anna Kolesárová |
| author_sort | Radko Mesiar |
| collection | DOAJ |
| description | In this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas. We show that there is a one-to-one correspondence between the classes of all quasi-copulas and 1-Lipschitz fuzzy implicators. A similar relation holds for copulas and 2-increasing 1-Lipschitz fuzzy implicators. Based on these relations, we introduce, discuss and exemplify several new construction methods for fuzzy implicators, and also discuss several dualities on the class of all 1-Lipschitz fuzzy implicators. In addition, we introduce a construction method for fuzzy implicators based on any two copulas and a Lebesgue integrable fuzzy implicator, and discuss some of its special cases. |
| first_indexed | 2024-04-13T06:57:24Z |
| format | Article |
| id | doaj.art-ebfd9e13ac5741f99c55b3cbe6b1ff42 |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-13T06:57:24Z |
| publishDate | 2020-06-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-ebfd9e13ac5741f99c55b3cbe6b1ff422022-12-22T02:57:13ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832020-06-0113110.2991/ijcis.d.200527.004Quasi-Copulas, Copulas and Fuzzy ImplicatorsRadko MesiarAnna KolesárováIn this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas. We show that there is a one-to-one correspondence between the classes of all quasi-copulas and 1-Lipschitz fuzzy implicators. A similar relation holds for copulas and 2-increasing 1-Lipschitz fuzzy implicators. Based on these relations, we introduce, discuss and exemplify several new construction methods for fuzzy implicators, and also discuss several dualities on the class of all 1-Lipschitz fuzzy implicators. In addition, we introduce a construction method for fuzzy implicators based on any two copulas and a Lebesgue integrable fuzzy implicator, and discuss some of its special cases.https://www.atlantis-press.com/article/125941266/viewCopulaFuzzy conjunctorFuzzy implicatorQuasi-copulaSemicopula |
| spellingShingle | Radko Mesiar Anna Kolesárová Quasi-Copulas, Copulas and Fuzzy Implicators International Journal of Computational Intelligence Systems Copula Fuzzy conjunctor Fuzzy implicator Quasi-copula Semicopula |
| title | Quasi-Copulas, Copulas and Fuzzy Implicators |
| title_full | Quasi-Copulas, Copulas and Fuzzy Implicators |
| title_fullStr | Quasi-Copulas, Copulas and Fuzzy Implicators |
| title_full_unstemmed | Quasi-Copulas, Copulas and Fuzzy Implicators |
| title_short | Quasi-Copulas, Copulas and Fuzzy Implicators |
| title_sort | quasi copulas copulas and fuzzy implicators |
| topic | Copula Fuzzy conjunctor Fuzzy implicator Quasi-copula Semicopula |
| url | https://www.atlantis-press.com/article/125941266/view |
| work_keys_str_mv | AT radkomesiar quasicopulascopulasandfuzzyimplicators AT annakolesarova quasicopulascopulasandfuzzyimplicators |