Let \({\mathcal B}\) be a \(\sigma\)-algebra on \(X\). An increasing function \(\mu:{\mathcal B}\to [0,1]\) with \(\mu(\emptyset)= 0\) and \(\mu(X)= 1\) is called a fuzzy measure. The authors study the question when for two fuzzy measures \(\mu\) and \(\nu\) on \({\mathcal B}\) there is an increasing function \(f: [0,1]\to [0,1]\) such that \(\nu= \mu\circ f\).