The annihilator of fuzzy subgroups

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...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 369; pp. 122 - 131
Main Authors Ardanza-Trevijano, S., Chasco, M.J., Elorza, J.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.08.2019
Subjects
B-algebra
Fuzzy annihilator subgroup
Fuzzy least squares
Fuzzy orthogonal complement
Fuzzy subgroup
Pontryagin duality
Pontryagin duality
Fuzzy subgroup
B-algebra
Fuzzy annihilator subgroup
Fuzzy orthogonal complement
Fuzzy least squares
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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.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2018.11.001