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Article | Open Access

Some Properties of the Extended Threshold Generated Implications

College of Mathematics and Information Science, Nanchang Normal University, Nanchang 330032, China
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
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Abstract

Fuzzy implications play an important role in both approximating reasoning and fuzzy control, and there are many generation methods for fuzzy implications for various applications. The extended threshold generation method for fuzzy implications can induce some implications differ from the usual implications, such as f-, g-implications, R-implications, S-implications, and those derived from the ordinal sum method. In this paper, we focus on the investigations of the preservation of some important properties under minimal necessary conditions similar to the e-threshold generation method, such as the neutral property, the exchange law, the weak importation law, the contraction law, and the distributivity property over t-norms and t-conorms.

Keywords

fuzzy implicationsextended threshold generationexchange principlelaw of importationcontraction lawdistributivity property

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Fuzzy Information and Engineering
Volume 16 Issue 3,
September 2024
Pages 175-193
DOI: 10.26599/FIE.2024.9270040
Cite this article:
Yi Z-H, Yao L-J, Qin F. Some Properties of the Extended Threshold Generated Implications. Fuzzy Information and Engineering, 2024, 16(3): 175-193. https://doi.org/10.26599/FIE.2024.9270040

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Received: 20 December 2023
Revised: 26 May 2024
Accepted: 07 June 2024
Published: 30 September 2024
© The Author(s) 2024. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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