  The study of mereology (parts and wholes) in the context of formal approaches
to vagueness can be approached in a number of ways. In the context of rough
sets, mereological concepts with a set-theoretic or valuation based ontology
acquire complex and diverse behavior. In this research a general rough set
framework called granular operator spaces is extended and the nature of
parthood in it is explored from a minimally intrusive point of view. This is
used to develop counting strategies that help in classifying the framework. The
developed methodologies would be useful for drawing involved conclusions about
the nature of data (and validity of assumptions about it) from antichains
derived from context. The problem addressed is also about whether counting
procedures help in confirming that the approximations involved in formation of
data are indeed rough approximations?
