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. 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