Approximation spaces in granular computing

Most data mining and granular computing systems extract knowledge or concept patterns from inexact and uncertain contexts. These patterns are usually approximated by a set of certain and exact components or granules. Therefore, research on approximation spaces becomes the bottleneck of granular computing and data mining. A variety of approximation spaces have been proposed and extensively investigated. Some typical approximation spaces are summarized and compared in this paper, including fuzzy sets, rough sets, near sets and neighborhood systems. Their characteristics and application domains are analyzed and compared. These approximation spaces are unified under the framework of neighbor systems.