Granulation and Nearest Neighborhoods: Rough Set Approach

“Nearest” neighborhoods are informally used in many areas of AI and database. Mathematically, a “nearest” neighborhood system that maps each object p a unique crisp/fuzzy subset of data, representing the “nearest” neighborhood, is a binary relation between the object and data spaces. “Nearest” neighborhood consists of data that are semantically related to p, and represents an elementary granule (atoms) of the system under consideration. This paper examines “rough set theory” of these elementary granules. Applications to databases, fuzzy sets and pattern recognition are used to illustrate the idea.