Fuzzy rough set model for set-valued data

In many practical situations, some of the attribute values for an object may be set-valued. The existing crisp rough set model for set-valued information systems is based on a tolerance relation that examines whether two set values have a non-empty intersection. Some information in the data will be lost according to the tolerance relation. Here we define a fuzzy relation and construct a fuzzy rough set model for set-valued information systems. The concepts of reduct, core, discernibility matrix and discernibility function for set-valued information systems, and relative reduct, core, discernibility matrix and discernibility function for set-valued decision systems are defined and examined. Attribute reduction in set-valued information systems based on discernibility matrices and functions are investigated.