| This paper discusses rough set theory and its applications in information systems. In chapter 2 and 3, two mathematical problems of rough set theory are discussed. In chapter 4 and 5, applications of rough set theory in two aspects are studied which are attribute reduct and the acquisition of the optimal decision rules in information systems. The whole paper is structured as follows.In chapter 2, the concept of "isolated point" is defined, whose influence on algebraic structure of rough set is demonstrated. Furthermore, rough equivalent classes are described by crisp sets and isolated points. In approximate space, the isolated point which consists one equivalent class itself is not contained in the boundary of any rough set. Hence, it plays an important and special role in the algebraic structure of rough sets. The discussion in this chapter illustrates such a problem that: each set generates an ordered pair of definable sets (the lower approximation and upper approximation) in approximate space, but for a certain ordered pair of definable sets, there may not exists any rough set corresponding to it.In chapter 3, the similarity measure of rough sets in approximate space is discussed. In approximation space, one equivalent class which is a minimal unit of recognition can be viewed as a knowledge granularity. Therefore, whether an object belongs to one set, or namely the degree of an object belonging to one set, is determined completely by the relationship between this set and the equivalent class containing the object. In other words, it is determined by the rough membership function. Using rough membership function, various similarity degrees of rough sets are proposed referring to the concepts of similarity degrees of fuzzy sets. Their properties are analyzed and their characteristics are compared.Chapter 4 discusses generalized decision reducts and the acquisition of optimal decision rules in general (consistent or inconsistent) decision...
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