Abstract
In this article, we present the study of
μ
-fuzzy subgroups and prove numerous fundamental algebraic attributes of this newly defined notion. We also define the concept of
μ
-fuzzy normal subgroup and investigate many vital algebraic characteristics of these phenomena. In addition, we characterize the quotient group induced by this particular fuzzy normal subgroup and establish a group isomorphism between the quotient groups
G
/
κ
μ
and
G
/
κ
∗
μ
. Furthermore, we initiate the study of level subgroup, open level subgroup, and tangible subgroup of a
μ
-fuzzy subgroup and emphasize the significance of
μ
-fuzzy normal subgroups by establishing a relationship between these newly defined notions and
μ
-fuzzy normal subgroup.