style="text-align:center; width:30%" border="1" |+ Sample Information System ! Object !! !! !! !! !! |- ! | 1 || 2 || 0 || 1 || 1 |- ! | 1 || 2 || 0 || 1 || 1 |- ! | 2 || 0 || 0 || 1 || 0 |- ! | 0 || 0 || 1 || 2 || 1 |- ! | 2 || 1 || 0 || 2 || 1 |- ! | 0 || 0 || 1 || 2 || 2 |- ! | 2 || 0 || 0 || 1 || 0 |- ! | 0 || 1 || 2 || 2 || 1 |- ! | 2 || 1 || 0 || 2 || 2 |- ! | 2 || 0 || 0 || 1 || 0 |} When the full set of attributes is considered, we see that we have the following seven equivalence classes or primitive (simple) concepts: Thus, the two objects within the first equivalence class, cannot be distinguished from one another based on the available attributes, and the three objects within the second equivalence class, cannot be distinguished from one another based on the available attributes. The remaining five objects are each discernible from all other objects. Now, let us imagine a projection of the attribute value system onto attribute alone, which would represent, for example, the view from an observer which is only capable of detecting this single attribute. Then we obtain the following much coarser equivalence class structure. This is in a certain regard the same structure as before, but at a lower degree of resolution (larger grain size). Just as in the case of value granulation (discretization/quantization), it is possible that relationships (dependencies) may emerge at one level of granularity that are not present at another. As an example of this, we can consider the effect of concept granulation on the measure known as attribute dependency (a simpler relative of the mutual information). To establish this notion of dependency (see also rough sets), let represent a particular concept granulation, where each is an equivalence class from the concept structure induced by attribute set . For example, if the attribute set consists of attribute alone, as above, then the concept structure will be composed of The dependency of attribute set on another attribute set , is given by That is, for each equivalence class in we add