  In relational approach to general rough sets, ideas of directed relations are
supplemented with additional conditions for multiple algebraic approaches in
this research paper. The relations are also specialized to representations of
general parthood that are upper-directed, reflexive and antisymmetric for a
better behaved groupoidal semantics over the set of roughly equivalent objects
by the first author. Another distinct algebraic semantics over the set of
approximations, and a new knowledge interpretation are also invented in this
research by her. Because of minimal conditions imposed on the relations,
neighborhood granulations are used in the construction of all approximations
(granular and pointwise). Necessary and sufficient conditions for the lattice
of local upper approximations to be completely distributive are proved by the
second author. These results are related to formal concept analysis.
Applications to student centered learning and decision making are also
outlined.
