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-fuzzy Annihilators in Residuated Lattices

  • Ariane G. Tallee Kakeu EMAIL logo , Lutz Strüngmann , Blaise B. Koguep Njionou and Celestin Lele
Published/Copyright: December 18, 2023
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ABSTRACT

In this paper, we provide a new characterization of -fuzzy ideals of residuated lattices, which allows us to describe -fuzzy ideals generated by -fuzzy sets. Thanks to the latter, we endow the lattice of -fuzzy ideals of a residuated lattice with suitable operations. Moreover, we introduce the notion of -fuzzy annihilator of an -fuzzy subset of a residuated lattice with respect to an -fuzzy ideal and investigate some of its properties. To this extent, we show that the set of all -fuzzy ideals of a residuated lattice is a complete Heyting algebra. Furthermore, we define some types of -fuzzy ideals of residuated lattices, namely stable -fuzzy ideals relative to an -fuzzy set, and involutory -fuzzy ideals relative to an -fuzzy ideal. Finally, we prove that the set of all stable -fuzzy ideals relative to an -fuzzy set is also a complete Heyting algebra, and that the set of involutory -fuzzy ideals relative to an -fuzzy ideal is a complete Boolean algebra.

2020 Mathematics Subject Classification: 03E72; 03G05; 03G10; 06D20

(Communicated by Anatolij Dvurečenskij)


Funding statement: The first author would like to thank the DAAD for their support.

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Received: 2022-11-05
Accepted: 2023-01-16
Published Online: 2023-12-18

© 2023 Mathematical Institute Slovak Academy of Sciences

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