Geodesic
Fuzzy implications based on quasi-copula and fuzzy negations
Souliotis, G.1 ; Rassias, M. Th. 2 ; Papadopoulos, B.1
1 Department of Civil Engineering, Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece
2 Hellenic Military Academy, Greece;Institute for Advanced Study, Princeton, USA
Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 2, p. 99-110.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.016.02.03
Classification : 03B52, 03B50, 94D05, 03E72
Keywords: Fuzzy implications, fuzzy negations, copula, quasi-copula, semi-copula, aggregations functions

Souliotis, G. 1 ; Rassias, M. Th.  2 ; Papadopoulos, B. 1

1 Department of Civil Engineering, Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece
2 Hellenic Military Academy, Greece;Institute for Advanced Study, Princeton, USA 
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Souliotis, G.; Rassias, M. Th. ; Papadopoulos, B. Fuzzy implications based on quasi-copula and fuzzy negations. Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 2, p. 99-110. doi : 10.22436/jnsa.016.02.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.02.03/

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