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

Naseem Ajmal () and Iffat Jahan ()
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Naseem Ajmal: University of Delhi
Iffat Jahan: University of Delhi

Fuzzy Information and Engineering, 2012, vol. 4, issue 2, 123-143

Abstract: Abstract 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.

Keywords: Fuzzy algebra; Normal fuzzy subgroup; Characteristic fuzzy subgroup; Commutator subgroup; Generated fuzzy subgroup; Lattices (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s12543-012-0106-0

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