An ordinary (transferable utility) game assigns to each coalition a real number, whereas each coalition of an interval game receives a compact nonempty interval. An interval game is size monotonic if the size of the interval of a smaller coalition is not larger than the size of the interval of a larger coalition. The authors generalize the center of gravity of the imputation set (CIS), the egalitarian nonseparable contribution value (ENSC), and the equal division rule (ED) in a natural way to a subclass of size monotonic interval games and call them ICIS, IENC, and IED. They deduce an algebraic formula for an arbitrary convex combination of these three solutions and show that it coincides, when interchanging the convex coefficients of ICIS and IENC, with the corresponding convex combination applied to dual interval games. Moreover, the interval Shapley value is defined and several illuminating examples and an application to a “transportation interval situation” are presented.