A study of normal fuzzy subgroups and characteristic fuzzy subgroups of a fuzzy group

In this paper, we investigate the properties of normal fuzzy subgroups of a fuzzy group. We also introduce the notion of a characteristic fuzzy subgroup of a fuzzy group, of which we provide level subset and strong level subset characterizations. Then we prove that a characteristic fuzzy subgroup of...

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Bibliographic Details
Published in:Fuzzy information and engineering 2012-06, Vol.4 (2), p.123-143
Main Authors: Ajmal, Naseem, Jahan, Iffat
Format: Article
Language:English
Subjects:
Commutators
Computational Intelligence
Engineering
Lattices
Original Article
Subgroups
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Summary:In this paper, we investigate the properties of normal fuzzy subgroups of a fuzzy group. We also introduce the notion of a characteristic fuzzy subgroup of a fuzzy group, of which we provide level subset and strong level subset characterizations. Then we prove that a characteristic fuzzy subgroup of a fuzzy group is a normal fuzzy subgroup. Besides we prove that the commutator subgroup generated by the commutator of two normal fuzzy subgroups of a fuzzy group is contained in their intersection. Finally, we construct many new lattices and sublattices of fuzzy subgroups and normal fuzzy subgroups of a given fuzzy group. We also construct lattices of characteristic fuzzy subgroups possessing sup-property.
ISSN:1616-8658
1616-8666
DOI:10.1007/s12543-012-0106-0