Abstract: Granular computing is an approach for knowledge representation and data mining. The key to granular computing is to make use of granules in problem solving. With the view point of granular computing, notion of a granule may be interpreted as one of the numerous small particles forming a larger unit. In many situations, there are different granules at different levels of scale in data sets having hierarchical scale structures. Therefore, the concept of multi-labeled information system is first introduced. Take into consideration the existence of incomplete information systems, a new function of granular information transformation is defined, and the concept of the incomplete multi-labeled information system is also proposed. With the function of granular information transformation, a hierarchical structure of granules can be obtained in incomplete multi-labeled information system. For each level, the similarity class can be defined by using similarity relation. Then the lower approximation and upper approximation of multi-granulation rough sets are defined by using similarity classes. Analogously, accuracy of approximations and roughness are also defined as usual at every level. Furthermore, the properties of lower approximations, upper approximations, accuracy of approximations and roughness between different levels are discussed respectively. Those properties may be useful to find laws of knowledge variation in multi-labeled incomplete information system while the granular size changing