In many practical situations, we need to make a decision under interval or set uncertainty: e.g., we need to decide how much we are willing to pay for an option that will bring us between $10 and $40, i.e., for which the set of possible gains is the interval S = [10,40]. To make such decisions, researcher have used the idea of additivity: that if have two independent options, then the price we pay for both should be equal to the sum of the prices that we pay for each of these options. It is known that this requirement enables us to make decisions for bounded closed sets S. In some practical situations, the set S of possible gains is not closed: e.g., we may know that the gain will be between $10 and $40, but always greater than $10 and always smaller than $40. In this case, the set of possible values in an open interval S = (10,40). In this paper, we show how to make decisions in situations of general -- not necessarily closed -- set uncertainty.