Fuzzy implications based on quasi-copula and fuzzy negations
Authors
G. Souliotis
- Department of Civil Engineering, Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece.
M. Th. Rassias
- Hellenic Military Academy, Greece.
- Institute for Advanced Study, Princeton, USA.
B. Papadopoulos
- Department of Civil Engineering, Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece.
Abstract
In this particular paper the connection of fuzzy implications to the basic concepts of probability theory such as copula, quasi-copula and semi-copula is being studied. This study showed that fuzzy implications produced through copula, quasi-copula or semi-copula, apart from having as a common characteristic the Lipschitz condition with constant 1, this characteristic is also the cornerstone for grouping fuzzy implications according to the original generator which is no other than a copula, quasi-copula or semi-copula.
Share and Cite
ISRP Style
G. Souliotis, M. Th. Rassias, B. Papadopoulos, Fuzzy implications based on quasi-copula and fuzzy negations, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 2, 99--110
AMA Style
Souliotis G., Rassias M. Th., Papadopoulos B., Fuzzy implications based on quasi-copula and fuzzy negations. J. Nonlinear Sci. Appl. (2023); 16(2):99--110
Chicago/Turabian Style
Souliotis, G., Rassias, M. Th., Papadopoulos, B.. "Fuzzy implications based on quasi-copula and fuzzy negations." Journal of Nonlinear Sciences and Applications, 16, no. 2 (2023): 99--110
Keywords
- Fuzzy implications
- fuzzy negations
- copula
- quasi-copula
- semi-copula
- aggregations functions
MSC
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