Abstract:
The concept of neighborhood system (NS) was first introduced to handle computer security and approximate retrieval in database and information retrieval (Lin, 1989a,b). When the label granular computing was introduced by the second author and Zadeh (Zadeh, 1998), NS was then used to model the local granule, namely, a granule is viewed as an uncertain region of or fuzzification of a point. In this paper, we shall (re-)define definitively the relevant concepts: major work is focused on rough sets (RS) relevant concepts, closure and interior. There are major efforts in RS community to axiomatize the closure (upper approximation) by right neighborhood (left neighborhood if the given neighborhood is left neighborhood); we disagree with this approach. We take topological approach; we need a new set of invariants. For simple case, such invariants are available and axiomatization can be done. All axiomatizations of RS can be done in this new setting; they will be reported in the future.
Tea Time: 3:30PM R707