up the size of its "lower approximation" (see rough sets) by the attributes in , i.e., More simply, this approximation is the number of objects which on attribute set can be positively identified as belonging to target set Added across all equivalence classes in the numerator above represents the total number of objects which—based on attribute set —can be positively categorized according to the classification induced by attributes . The dependency ratio therefore expresses the proportion (within the entire universe) of such classifiable objects, in a sense capturing the "synchronization" of the two concept structures and The dependency "can be interpreted as a proportion of such objects in the information system for which it suffices to know the values of attributes in to determine the values of attributes in " (Ziarko & Shan 1995). Having gotten definitions now out of the way, we can make the simple observation that the choice of concept granularity (i.e., choice of attributes) will influence the detected dependencies among attributes. Consider again the attribute value table from above: {| class="wikitable" 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 |} Consider the dependency of attribute set on attribute set That is, we wish to know what proportion of objects can be correctly classified into classes of based on knowledge of The equivalence classes of and of are shown below. {| class="wikitable" |- ! ! |- | | |} The objects that can be definitively categorized according to concept structure based on are those in the set and since there are six of these, the dependency of on , This might be considered an interesting dependency in its own right, but