On Fuzzy Negations and Laws of Contraposition. Lattice of Fuzzy Negations-Reference-Cited by-同舟云学术

On Fuzzy Negations and Laws of Contraposition. Lattice of Fuzzy Negations

Published:2023-09-01 Issue:1 Volume:31 Page:151-159
ISSN:1898-9934
Container-title:Formalized Mathematics
language:en
Short-container-title:

Author:

Grabowski Adam¹

Affiliation:

1. 1 Faculty of Computer Science , University of Białystok , Poland

Abstract

Summary This the next article in the series formalizing the book of Baczyński and Jayaram “Fuzzy Implications”. We define the laws of contraposition connected with various fuzzy negations, and in order to make the cluster registration mechanism fully working, we construct some more non-classical examples of fuzzy implications. Finally, as the testbed of the reuse of lattice-theoretical approach, we introduce the lattice of fuzzy negations and show its basic properties.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics

Link

https://www.sciendo.com/pdf/10.2478/forma-2023-0014

Reference15 articles.

1. Michał Baczyński and Balasubramaniam Jayaram. Fuzzy Implications. Springer Publishing Company, Incorporated, 2008. doi:10.1007/978-3-540-69082-5.

2. Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.

3. Józef Drewniak. Invariant fuzzy implications. Soft Computing, 10:506–513, 2006.

4. Didier Dubois and Henri Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.

5. Adam Grabowski. Formal introduction to fuzzy implications. Formalized Mathematics, 25(3):241–248, 2017. doi:10.1515/forma-2017-0023.

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