In engineering, we constantly need to make decisions: which design to select, which parameters to select for this design, etc.
The traditional approach to decision making is based on the assumption that we know all possible consequences of each alternative, and we know the probability of each such consequence. Under this assumption, we can describe a rational decision-making process: to each possible consequence, we assign a numerical values called its utility, and we select the alternative for which the expected value of the utility is the largest.
An important advantage of this approach is that it can be performed in real time: if after we made a decision, a new alternative appears, we do not need to repeat the whole analysis again: all we need to do is compare the new alternative with the previously selected ones.
In the past, when we used the same procedures year after year, we accumulated a lot of data about the consequences of different decisions -- based from which we could estimate the desired probabilities. Nowadays, with new technologies, new materials constantly emerging, we do not have such detailed information about the consequences of these new technologies. As a result, we often only have partial information about the corresponding probabilities. Different possible probability values result in different values of expected utility. Hence, for each alternative, instead of a single value of expected utility, we have a range (interval) of possible values. We need to make a decision under such interval uncertainty.
In this paper, we describe when we can make decisions under interval uncertainty in linear time and in real time -- and when we cannot.