An incomplete interval-valued information system (IIVIS) is an information system (IS) in which the information values are interval numbers with missing values. This article researches information structures in an IIVIS. First, information structures in an IIVIS are obtained. In addition, the dependence and information distance are presented. The properties of information structures are investigated. Furthermore, group and lattice characterizations of information structures in an IIVIS are studied. Lastly, the-rough entropy is explored as an application of the proposed information structures.
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