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A Method of Generating Fuzzy Implications with Specific Properties

Section of Mathematics and Informatics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Kimeria, Greece
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Symmetry 2020, 12(1), 155; https://doi.org/10.3390/sym12010155
Received: 24 December 2019 / Revised: 6 January 2020 / Accepted: 8 January 2020 / Published: 12 January 2020
In this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are invariant via this method. Furthermore, we suggest some ways of preservation or violation of these properties, based in this method. We show how we can generate not greater or not weaker fuzzy implications with specific properties. Finally, two subclasses of any fuzzy implication arise, the so called T and S subclasses.
Keywords: fuzzy implication; t-norm; t-conorm fuzzy implication; t-norm; t-conorm
MDPI and ACS Style

Grammatikopoulos, D.S.; Papadopoulos, B.K. A Method of Generating Fuzzy Implications with Specific Properties. Symmetry 2020, 12, 155.

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