In many practical situations, measurements are characterized by interval uncertainty -- namely, based on each measurement result, the only information that we have about the actual value of the measured quantity is that this value belongs to some interval. If several such intervals -- corresponding to measuring the same quantity -- have an empty intersection, this means that at least one of the corresponding measurement results is an outlier, caused by a malfunction of the measuring instrument. From the purely mathematical viewpoint, if the intersection is non-empty, there is no reason to be suspicious, but from the practical viewpoint, if the intersection is too narrow -- i.e., almost empty -- then we should also be suspicious. To be on the safe side, it is desirable to take the second measurement into account only if we are sufficiently sure that this measurement is not an outlier. In this paper, we describe a natural way to formalize this idea.