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The annihilator of fuzzy subgroups. (English) Zbl 1423.20071
Summary: We implement the notion of annihilator into fuzzy subgroups of an abelian group. There are different uses for the term annihilator in algebraic contexts that have been used fuzzy systems. In this paper, we refer to another type of annihilator which is essential in classical duality theory and extends the widely applied notion of orthogonal complement in Euclidean spaces. We find that in the natural algebraic duality of a group, a fuzzy subgroup can be recovered after taking the inverse annihilator of its annihilator. We also study the behavior of annihilators with respect to unions and intersections. Some illustrative examples of annihilators of fuzzy subgroups are shown, both with finite and infinite rank.
20N25 Fuzzy groups
20K27 Subgroups of abelian groups
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
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