International Journal of Computational Intelligence Systems

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Volume 13, Issue 1, 2020, Pages 681 - 689

Quasi-Copulas, Copulas and Fuzzy Implicators

Authors
Radko Mesiar1, 2, *, ORCID, Anna Kolesárová3
1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia
2University of Ostrava, Institute for Research and Applications of Fuzzy Modelling, 30. Dubna 22, 701 03 Ostrava, Czech Republic
3Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia
*Corresponding author. Email: radko.mesiar@stuba.sk
Corresponding Author
Radko Mesiar
Received 16 April 2020, Accepted 12 May 2020, Available Online 16 June 2020.
DOI
10.2991/ijcis.d.200527.004How to use a DOI?
Keywords
Copula; Fuzzy conjunctor; Fuzzy implicator; Quasi-copula; Semicopula
Abstract

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.

Copyright
© 2020 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
13 - 1
Pages
681 - 689
Publication Date
2020/06/16
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.d.200527.004How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Radko Mesiar
AU  - Anna Kolesárová
PY  - 2020
DA  - 2020/06/16
TI  - Quasi-Copulas, Copulas and Fuzzy Implicators
JO  - International Journal of Computational Intelligence Systems
SP  - 681
EP  - 689
VL  - 13
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.200527.004
DO  - 10.2991/ijcis.d.200527.004
ID  - Mesiar2020
ER  -