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Rough set theory has been considered as a useful tool to deal with inexact, uncertain, or vague knowledge. In real-world, most of information systems are based on dominance relations, called ordered information systems. Although some uncertainty measures to evaluate the uncertainty of rough sets have been investigated in ordered information systems, the existing measures are not able to characterize well the imprecision of a rough set. So, it is necessary to find a new method to measure the roughness of rough sets in ordered information systems. In this paper, we give a well-justified measure, and some important properties are investigated. By an example, it is shown that our new method does not only overcome the limitations of the existing measures but also consist with human cognition in ordered information systems.