Pure rough mereology and counting

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?