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.
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