On algebraic aspects of η-fuzzy subgroups

In this paper, we define the term η-fuzzy subgroup and show that every fuzzy subgroup is a η-fuzzy subgroup. We define some of the algebraic properties of the concept of η-fuzzy cosets. Furthermore, we initiate the study of the η-fuzzy normal subgroup and the quotient group with respect  to the η-fuzzy normal subgroup and demonstrate some of their various group theoretical properties.