Algebraic Properties of λ-Fuzzy Subgroups

Abstract

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

Key words and phrases. fuzzy subgroup; fuzzy normal subgroup; λ-fuzzy subgroup; λ-fuzzy coset; λ-fuzzy normal subgroup.

1991 Mathematics Subject Classification. 03E72; 08A72; 20N25