In many theories and applications with uncertainty, using intervals to characterize uncertainty is simple and operable. It is crucial to choose a proper order for an interval method. In general, a total order is superior to a partial order for those applications in which we have to make a final decision. Motivated by this idea, we generalized interval-valued monotone comparative statics (MCS) with a partial order to interval-valued MCS with a total order, to be more precise, with an admissible order. The generalization was not trival. We obtained a necessary and sufficient condition for MCS by a series of new concepts such as an interval-valued quasi-super-modular function and an interval-valued single crossing property with an admissible order. The same condition was only sufficient in the existing literature. Furthermore, we illustrated the efficiency of the interval-valued MCS with the lexicographical orders and XY-order, which are well-known admissible orders. Finally, we applied our results in interval games with strategic complements to get the monotonity of the best response correspondence for player $i$.