Let \([I]\) be the set of all closed subintervals of the unit interval. The set is ordered by the relation \([a,b]\leq [c,d]\) if and only if \(a\leq c\) and \(b\leq d\). An \([I]\)-valued mapping \(\mu\) defined on a \(\sigma\)-algebra is called interval-valued measure, if \(\mu(\emptyset)= [0,0]\), \(\mu(X)= [1,1]\), \(\mu\) is monotone and continuous from below. The main result of the paper states that any \([I]\)-valued measure can be extended to the set of all \([I]\)-valued fuzzy sets by means of Sugeno’s integral.