A Study of GD ? - Implications, a New Hyper Class of Fuzzy Implications

Dimitrios S. Grammatikopoulos and Basil Papadopoulos
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Dimitrios S. Grammatikopoulos: Section of Mathematics and Informatics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Kimmeria, Greece
Basil Papadopoulos: Section of Mathematics and Informatics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Kimmeria, Greece

Mathematics, 2021, vol. 9, issue 16, 1-16

Abstract: In this paper, we introduce and study the GD ? -operations, which are a hyper class of the known D ? -operations. GD ? -operations are in fact D ? -operations, that are generated not only from the same fuzzy negation. Similar with D ? -operations, they are not always fuzzy implications. Nevertheless, some sufficient, but not necessary conditions for a GD ? -operation to be a fuzzy implication, will be proved. A study for the satisfaction, or the violation of the basic properties of fuzzy implications, such as the left neutrality property, the exchange principle, the identity principle and the ordering property will also be made. This study also completes the study of the basic properties of D ? -implications. At the end, surprisingly an unexpected new result for the connection of the QL-operations and D-operations will be presented.

Keywords: fuzzy implication; D ? -implication; fuzzy negation; t-norm; t-conorm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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