Lattice-theoretic ideals have been used to define and generate non granularrough approximations over general approximation spaces over the last few yearsby few authors. The goal of these studies, in relation based rough sets, havebeen to obtain nice properties comparable to those of classical roughapproximations. In this research paper, these ideas are generalized in a severeway by the present author and associated semantic features are investigated byher. Granules are used in the construction of approximations in implicit waysand so a concept of co-granularity is introduced. Knowledge interpretationassociable with the approaches is also investigated. This research will be ofrelevance for a number of logico-algebraic approaches to rough sets thatproceed from point-wise definitions of approximations and also for usingalternative approximations in spatial mereological contexts involving actualcontact relations. The antichain based semantics invented in earlier papers bythe present author also applies to the contexts considered.
展开▼
