A new concept in fuzzy sets theory, namely that of gradual element, was introduced recently. It is known that the set of gradual real numbers is not ordered linearly. We restrict our attention to a discrete case and propose a class of linear orders for discrete gradual real numbers. Then, using idea of the so-called admissible order of intervals, we present a class of linear orders for discrete gradual intervals. Once we have the linear orders it is possible to define OWA operator for discrete gradual real numbers and OWA operator for discrete gradual intervals. Recall that gradual intervals also encompass fuzzy intervals, hence our results are applicable to the setting of fuzzy intervals. Our approach is illustrated on a multi-expert decision making problem.
OWA operator, ordered weighted averaging operator, gradual number, gradual interval, fuzzy interval, linear order, total order, multi-expert decision making, type-2 fuzzy set