Decision Making Under Interval Uncertainty as a Natural Example of a Quandle

In many real-life situations, we need to select an alternative from a set of possible alternatives. In many such situations, we have a well-defined objective function u(a) that describes our preferences. If we know the exact value of u(a) for each alternative a, then we select the alternative with the largest value of u(a). In practice, however, we usually know the consequences of each decision a only with some uncertainty. As a result, for each alternative a, instead of the exact utility value u(a), we only know the interval of possible values [u(a), u(a)]. In this paper, we show that the resulting problem of decision making under interval uncertainty is a natural example of a quandle, i.e., of a general class of operations introduced in knot theory. 1 Need for Decision Making under Interval Uncertainty Need for decision making. In many real-life situations, we need to select an alternative a from the list of possible alternatives – e.g., we want to select a design and/or location of a plant, a financial investment, etc. In many such situations, we have a well-defined objective function u(a) that describes our preferences. If we know the exact value of u(a) for each alternative a, then we select the alternative with the largest value of u(a). Decision making under interval uncertainty. In practice, we usually only know the consequences of each decision with some uncertainty. Often, the only information that we have about the corresponding values of u(a) is that it is somewhere between the known bounds u(a) and u(a), i.e., that u(a) ∈ [u(a), u(a)]. How can we make a decision under such interval uncertainty?