Fuzzy implications based on quasi-copula and fuzzy negations

Volume 16, Issue 2, pp 99--110 http://dx.doi.org/10.22436/jnsa.016.02.03

Publication Date: July 31, 2023 Submission Date: October 12, 2022 Revision Date: January 19, 2023 Accteptance Date: March 03, 2023

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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.

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Keywords

• Fuzzy implications
• fuzzy negations
• copula
• quasi-copula
• semi-copula
• aggregations functions

MSC

•  03B52
•  03B50
•  94D05
•  03E72

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