Ariane G. Tallee Kakeu, L. Strüngmann, B. B. Koguep Njionou, Celestin Lele
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ABSTRACT In this paper, we provide a new characterization of ℒ-fuzzy ideals of residuated lattices, which allows us to describe ℒ-fuzzy ideals generated by ℒ-fuzzy sets. Thanks to the latter, we endow the lattice of ℒ-fuzzy ideals of a residuated lattice with suitable operations. Moreover, we introduce the notion of ℒ-fuzzy annihilator of an ℒ-fuzzy subset of a residuated lattice with respect to an ℒ-fuzzy ideal and investigate some of its properties. To this extent, we show that the set of all ℒ-fuzzy ideals of a residuated lattice is a complete Heyting algebra. Furthermore, we define some types of ℒ-fuzzy ideals of residuated lattices, namely stable ℒ-fuzzy ideals relative to an ℒ-fuzzy set, and involutory ℒ-fuzzy ideals relative to an ℒ-fuzzy ideal. Finally, we prove that the set of all stable ℒ-fuzzy ideals relative to an ℒ-fuzzy set is also a complete Heyting algebra, and that the set of involutory ℒ-fuzzy ideals relative to an ℒ-fuzzy ideal is a complete Boolean algebra.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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