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Algebraic properties of \(\lambda\)-fuzzy subgroups. (English) Zbl 1449.20077

Summary: In this paper, we initiate the study of \(\lambda\)-fuzzy sets. We define the notion of \(\lambda\)-fuzzy subgroup and prove that every fuzzy subgroup is \(\lambda\)-fuzzy subgroup. We introduce the notion of \(\lambda\)-fuzzy cosets and establish their algebraic properties. We also initiate the study of \(\lambda\)-fuzzy normal subgroups and quotient group with respect to \(\lambda\)-fuzzy normal subgroup and prove some of their various group theoretic properties. We also investigate effect on the image and inverse image of \(\lambda\)-fuzzy subgroup (normal subgroup) under group homomorphism and establish an isomorphism between the quotient group with respect to \(\lambda\)-fuzzy normal subgroup and quotient group with respect to the normal subgroup \(G_{\rho^\lambda}\).

MSC:

20N25 Fuzzy groups
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