Recent development in the design of multi-dimensional transfer functions allows us to automatically generate comprehensible visualization images of given volumes by taking into account local features such as differentials and curvatures. However, especially when visualizing volumes obtained by scientific simulations, observers usually exploit their knowledge about the simulation settings as the clues to the effective control of visualization parameters for their own specific purposes. This paper therefore presents an objective-based framework for visualizing simulated volume datasets by introducing a new set of topological attributes. These topological attributes are calculated from the level-set graph of a given volume dataset, and thus differ from the conventional local attributes in that they also illuminate the global structure of the volume. The present framework provides a systematic means of emphasizing the underlying volume features, such as nested structures of isosurfaces, configuration of isosurface trajectories, and transitions of isosurface's topological type. Several combinations of the topological attributes together with the associated transfer function designs are devised and applied to real simulated datasets in order to demonstrate the feasibility of the present framework.