Uncertainty Measurement Of Ordered Information System

The uncertainty measurement of information system is one of important issues in the field of information science, and many reserchers of home and overseas have pay more attention to it in recent years. In the paper, with rough set theory as background, ordered information system as research object, the uncertainty measurement is further studied based on dominance relation in ordered information system, and the following results are obtained.Based on algebra viewpoint, in the paper, we first propose four kinds of dual upper and lower approximation operators and corresponing accuracy, roughness and approximation accuracy in ordered information system, then dual approximation operators are extended and two kinds of non-dual upper and lower approximation operators and corresponing accuracy, roughness and approximation accuracy are proposed, and the properties of six kinds of upper and lower approximation operators and corresponing measures are studied, theoreretical analysis indicates that these measures have monotonicity with knowledge become crarser or finer.therefore, they can be used to measure the uncertainty of ordered information system. Finally, six kinds of upper and lower approximation operators and corresponing measures are analyzed and compared, the results showed that accuracy of the types of first, second, fourth and fifth are higher than that the types of third, sixth, and effecive of conclusion have been illustrated by examples.Based on information viewpoint, two kinds of uncertainty measures are proposed in the paper. Based on upper and lower approximation operators, we first define a new information entropy and information co-entropy in ordered information system, it has been proved that properties of the new information entropy and information co-entropy are also have monotonicity with knowledge become crarser or finer, so they can be used to measure the uncertainty of ordered information system; then the similarity of sets are considered, the concept of knowledge similarity of ordered information system is introduced, and properties of knowledge similarity are analysed, the result indicates that knowledge similarity can also measure the uncertainty of ordered information system; finally, the effeciveness of these two kinds of uncertainty measures have been illustrated by examples.