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...

Full description

Bibliographic Details
Main Authors:	Radko Mesiar, Anna Kolesárová
Format:	Article
Language:	English
Published:	Atlantis Press 2020-06-01
Series:	International Journal of Computational Intelligence Systems
Subjects:	Copula Fuzzy conjunctor Fuzzy implicator Quasi-copula Semicopula
Online Access:	https://www.atlantis-press.com/article/125941266/view

id	doaj-ebfd9e13ac5741f99c55b3cbe6b1ff42
record_format	Article
spelling	doaj-ebfd9e13ac5741f99c55b3cbe6b1ff422020-11-25T03:02:24ZengAtlantis PressInternational Journal of Computational Intelligence Systems 1875-68832020-06-0113110.2991/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
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Radko Mesiar Anna Kolesárová
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
author_facet	Radko Mesiar Anna Kolesárová
author_sort	Radko Mesiar
title	Quasi-Copulas, Copulas and Fuzzy Implicators
title_short	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_sort	quasi-copulas, copulas and fuzzy implicators
publisher	Atlantis Press
series	International Journal of Computational Intelligence Systems
issn	1875-6883
publishDate	2020-06-01
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.
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
_version_	1724689786221887488

Quasi-Copulas, Copulas and Fuzzy Implicators

Similar Items