Uncertainty Measurement for a Hybrid Information System With Images: An Application in Attribute Reduction

A hybrid information system with images (HISI) is an information system (IS) where there exist many kinds of data or attributes (e.g., boolean, categorical, real-valued, set-valued, interval-valued, imaged, decision and missing data or attributes). Uncertainty measurement (UM) is an effective tool for evaluation. This article inquires into UM for a HISI with application to attribute reduction. The distance between attribute values in a HISI is first constructed. Then, the tolerance relations on an object set of a HISI are obtained by means of this distance. Next, information structures in a HISI are proposed. After that, UM for a HISI is considered by using its information structures. Moreover, effectiveness analysis for the proposed measures is conducted from the angle of statistics. Finally, an application of the proposed measures in attribute reduction for a HISI is given, and the corresponding algorithms are put forward.