  Rational approximations are introduced and studied in granular graded rough
sets and generalizations thereof by the first author in recent research papers.
The concept of rationality is determined by related ontologies and coherence
between granularity, mereology and approximations in the context. In addition,
a framework for rational approximations is introduced by her in the mentioned
paper(s). Granular approximations constructed as per the procedures of variable
precision rough sets (VPRS) are likely to be more rational than those
constructed from a classical perspective under certain conditions. This may
continue to hold for some generalizations of the former. However, a formal
characterization of such conditions is not available in the previously
published literature. In this research, theoretical aspects of the problem are
critically examined, uniform generalizations of granular VPRS are introduced,
new connections with granular graded rough sets are proved, appropriate
concepts of substantial parthood are introduced, their extent of compatibility
with the framework is accessed, and the framework is extended. Basic
assumptions are explained in detail, and additional examples are constructed
for readability. Furthermore, meta applications to cluster validation, image
segmentation and dynamic sorting are invented. Extensions to direct
generalizations of VPRS such as probabilistic rough sets are a natural
consequence of the work.
