First GrC model - Neighborhood Systems the most general rough set models

Neighborhood System(NS) is revisited from the view of Formal GrC Model. NS formalize the ancient intuition, infinitesimals, which led to the invention of calculus, topology and non-standard analysis. In this paper, we show that Ziarko's variable precision model can be expressed by NS. Together with previously known results (NS includes topology, binary relation(binary neighborhood system) and covering as special cases), NS is the most general rough set model. A new operation “and” is introduced that generates a base of a topology; we will call it knowledge base. The approximations based on such knowledge base can be interpreted as learning. This is different from traditional rough set approximations.