Shuaib, Umer; Asghar, Wassem Algebraic properties of \(\lambda\)-fuzzy subgroups. (English) Zbl 1449.20077 Jordan J. Math. Stat. 12, No. 2, 115-134 (2019). 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 Keywords:fuzzy subgroup; fuzzy normal subgroup; \(\lambda\)-fuzzy subgroup; \(\lambda\)-fuzzy coset; \(\lambda\)-fuzzy normal subgroup PDFBibTeX XMLCite \textit{U. Shuaib} and \textit{W. Asghar}, Jordan J. Math. Stat. 12, No. 2, 115--134 (2019; Zbl 1449.20077) Full Text: Link