9.9 rough Set theory 263 9.9 rough Set theory Rough set theory is a relatively recent development in the field of artificial intelligence.The notion of rough sets was introduced by Zdzislaw Pawlak in his seminal paper (Pawlak, 1982). This theory is useful for discovering rela- tionships in data and to reason about incomplete data. It is a formal theory derived from basic research on logical properties of information systems. Rough sets are built on ordinary sets. Obviously, rough sets and fuzzy sets are complementary generalizations of classical sets. The approximation spaces of rough set theory are sets with multiple memberships, while fuzzy sets are concerned with partial memberships. The speedy progress of the rough set approach provides a vital basis for soft computing. In order to understand and use raw data, we derive essential knowledge about it. This knowledge can be represented in various forms, such as rules, algorithms, and equations. However, it is not always essential to derive con- clusions from whole data. This means that only rough data or coarse data may be enough. Sometimes, such approximate rough data may be better than detailed data. The rough set theory presents a novel approach for reasoning