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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.A rough set, first described by Zdzis aw I. Pawlak, is a formal approximation of a crisp set (i.e., conventional set) in terms of a pair of sets which give the lower and the upper approximation of the original set. In the standard version of rough set theory (Pawlak 1991), the lower- and upper-approximation sets are crisp sets, but in other variations, the approximating sets may be fuzzy sets. This section contains an explanation of the basic framework of rough set theory (proposed originally by Zdzis aw I. Pawlak), along with some of the key definitions. A review of this basic material can be found in sources such as Pawlak (1991), Ziarko (1998), Ziarko & Shan (1995), and many others.