A four-hybrid information system (4HIS) is an information system (IS) where the dataset of object descriptions consists of categorical, boolean, real-valued and missing data or attributes. This paper studies measures of uncertainty for a 4HIS and its application in attribute reduction. The distance function for each type of attribute in a 4HIS is first provided. Then, this distance is used to produce the tolerance relation induced by a given subsystem in a 4HIS. Next, information structure of this subsystem is proposed in terms of a set vector and dependence between information structures is introduced. Moreover, granulation and entropy measures in a 4HIS are investigated on the basis of information structures. In order to verify the feasibility of the proposed measures, effectiveness analysis is performed from a statistical perspective. Finally, an application of the proposed measures for attribute reduction in a 4HIS is given.