Real-world data collections are often heterogeneous (represented by a set of mixed attributes data types: numerical, categorical and fuzzy); since most available similarity measures can only be applied to one type of data, it becomes essential to construct an appropriate similarity measure for comparing such complex data. In this paper, a framework of new and unified similarity measures is proposed for comparing heterogeneous objects described by numerical, categorical and fuzzy attributes. Examples are used to illustrate, compare and discuss the applications and efficiency of the proposed approach to heterogeneous data comparison and clustering.