We pursue the work by M. Fontana, K.A. Loper and R. Matsuda. Let D be an integral domain, let F(D) (resp., f(D)) be the set of non-zero (resp., finitely generated) fractional ideals of D, let ? be a semistar operation on D. They showed that if ? satisfies (F F1)? = (F F2)? implies F?1 = F?2 for every F, F1, F2 ∈ f(D), then ? need not satisfy (F G1)? = (F G2)? implies G?1 = G?2 for every F ∈ f(D) and every G1, G2 ∈ F(D). In this paper, we show its analogy for monoids.