Granular Computing using Neighborhood Systems

A set-theoretic framework is proposed for granular computing. Each element of a universe is associated with a nonempty family of neighborhoods. A neighborhood of an element consists of those elements that are drawn towards that element by indistinguishability, similarity, proximity, or functionality. It is a granule containing the element. A neighborhood system is a family of granules, which is the available information or knowledge for granular computing. Operations on neighborhood systems, such as complement, intersection, and union, are defined by extending set-theoretic operations. They provide a basis of the proposed framework of granular computing. Using this framework, we examine the notions of rough sets and qualitative fuzzy sets.