A new roughness measure in ordered information systems

Rough set theory is a valid mathematical tool to deal with inexact, uncertain, or vague knowledge. 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. In order 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 reflect well the uncertainty of rough sets, but also consist with human cognition in ordered information systems.