Let (X, F, g) be a fuzzy measure space. Then for any h$in$ $L^{0}$ (X) , a$in$[0 , 1] , and $Ain$F ∫$_{A}$aㆍh($chi$)┬g＝aㆍ∫$_{A}$h($chi$)┬g with the t-seminorm ┬(x, y)= xy. And we prove that the Seminormed fuzzy integral has some linearity properties only for ｛0,1｝-classes of fuzzy measure as follow, For any f, h$in$ $L^{0}$ ($chi$), any a, b$in$R+: af＋bh$in$ $L^{0}$ ($chi$)⇒ ∫$_{A}$(af＋bh)┬g＝a∫$_{A}$f┬g＋b∫$_{A}$h┬g; if and only if g is a probability measure fulfilling g(A) $in$｛0, 1｝ for all $Ain$F.n$</TEX>F.