Note on the lack of equality between fuzzy weighted average and fuzzy convex sum

The paper shows that the equality of the interval-valued weighted average based on interval weights and the convex sum based on normalized interval weights presented in Dubois [The role of fuzzy sets in decision sciences: old techniques and new directions, Fuzzy Sets Syst. 184 (2011) 3–28] is generally false for n ≥ 3 and discusses its consequences.