This paper discuss some properties of non-monotonic fuzzy measures of
Phi-bounded variation. We show that there is an example of Phi such th
at BV(X,F) is a proper subspace of Phi BV(X,F). And also, we prove tha
t Phi BV(X,F) is a real Banach space. Furthermore, we investigated som
e properties of non-monotonic fuzzy Phi-measures.