Uncertainty is usually gauged by using standard statistical characteristics: mean, variance, correlation, etc. Then, we use the known values of these characteristics (or the known bounds on these values) to select a decision. Sometimes, it becomes clear that the selected characteristics do not always describe a situation well; then other known (or new) characteristics are proposed. A good example is description of volatility in finance: it started with variance, and now many descriptions are competing, all with their own advantages and limitations.
In such situations, a natural idea is to come up with characteristics tailored to specific application areas: e.g., select the characteristic that maximize the expected utility of the resulting risk-informed decision making.
With the new characteristics, comes the need to estimate them when the sample values are only known with interval uncertainty. Algorithms originally developed for estimating traditional characteristics can often be modified to cover new characteristics.