The annihilator of fuzzy subgroups

Autores: Ardanza-Trevijano Moras, Sergio; Chasco Ugarte, María Jesús; Elorza Barbajero, Jorge (Autor de correspondencia)
Título de la revista: FUZZY SETS AND SYSTEMS
ISSN: 0165-0114
Volumen: 369
Páginas: 122 - 131
Fecha de publicación: 2019
Lugar: WOS
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.