Attribute selection approaches for incomplete interval-value data

Attribute selection in an information system (IS) is an important issue when dealing with a large amount of data. An IS with incomplete interval-value data is called an incomplete interval-valued information system (IIVIS). This paper proposes attribute selection approaches for an IIVIS. Firstly, the similarity degree between two information values of a given attribute in an IIVIS is proposed. Then, the tolerance relation on the object set with respect to a given attribute subset is obtained. Next, θ-reduction in an IIVIS is studied. What is more, connections between the proposed reduction and information entropy are revealed. Lastly, three reduction algorithms base on θ-discernibility matrix, θ-information entropy and θ-significance in an IIVIS are given.