This paper discussed a new parameter in the fuzzy graph FG = (Ω, η). This parameter is named the cutoff fuzzy domination number and is represented by (γcf) and tested in a strong fuzzy graph. Some features and limitations of this parameter are presented, such as the fuzzy path, cycle, complete, complete bipartite, wheel, and star. In addition, the relation between this parameter and other known concepts in fuzzy graphs is introduced.