Summary: This paper is concerned with a fuzzy stopping time for a dynamic fuzzy system. A new class of fuzzy stopping times, called monotone fuzzy stopping times, is introduced. The notion of monotonicity is well known and important in stochastic optimization theory. Here we try to define a monotone property and discuss a stopping problem which is a corresponding dynamic fuzzy system. Since the fuzzy stopping time can be constructed using \(\alpha\)-cuts of fuzzy states, the explicit derivation of an optimal one is derived under appropriate assumptions. The key point of our discussion for the optimization of a stopping problem is to induce an additive weighting function for the fuzzy reward.