Uncertainty Measurement for a Grey Information System

A grey information system (GIS) is a new kind of IS. Uncertainty measurement (UM) can provide a new perspective for data analysis and help to reveal the essential features of data. This article studies UM for a GIS. The main work of this paper includes: first, the similarity degree between two information values of each attribute in a GIS is constructed. And then, the tolerance relation induced by a given subsystem is acquired by the similarity degree. After that, the information structure of this subsystem is brought forward. Additionally, measures of uncertainty for a GIS are explored. Moreover, the optimal selection of information structures based on the proposed uncertainty measures is studied and the application of these measures is displayed. Finally, to verify the validity of these measures, statistical effectiveness analysis is carried out. These results will help us understand the intrinsic properties of uncertainty in a GIS.