Abstract: Uncertainty measurement is one of the major research problems in rough set theory, and the entropy measure has caught many attentions. However, there is still less research about Shannon entropy measure with monotonicity for interval-valued information systems. For this purpose, firstly, this paper proposes a method of inducing a partition from a given covering and proves that the finer the covering, the finer the partition derived from it, so that partition entropy can be used to measure the uncertainty of interval-valued information system. Secondly, the Shannon entropy measure and the co-entropy (granularity) measure for interval-valued information systems are constructed respectively, and their monotonicity and boundedness are proved. At last, the relationship between Shannon entropy and co-entropy is analyzed.