Neighborhood systems: mathematical models of information granulations

The notion of neighborhood systems (NS), which is an abstraction of "near" or "negligible distance," is used to model information granulation. A granule at a point (object) p consists of a clump (crisp/fuzzy set) of data that are related or near the point p. Mathematically, NS, by its definition, includes topological spaces (TS) and rough sets (RS) as special cases. The deeper part of NS is its ability in representing the context dependent notion of near-ness or approximation (via small granule). We apply the idea to formulate the notion of qualitative fuzzy sets.