Rough sets and data analysis

In this talk we are going to present basic concepts of a new approach to data analysis, called rough set theory(13). The theory has attracted attention of many researchers and practitioners all over the world, who contributed essentially to its development and applications. Rough set theory overlaps with many other theories, especially with fuzzy set theory(2,15), evidence theory(19) and Boolean reasoning methods(18), discriminant analysis(5) - nevertheless it can be viewed in its own rights, as an independent, complementary, and not competing discipline. Rough set theory is based on classification. Consider, for example, a group of patients suffering from a certain disease. With every patient a data file is associated containing information like, e.g. body temperature, blood pressure, name, age, address and others. All patients revealing the same symptoms are indiscernible (similar) in view of the available information and can be classified in blocks, which can be understood as elementary granules of knowledge about patients (or types of patients). These granules are called elementary sets or concepts, and can be considered as elementary building blocks of knowledge about patients. Elementary concepts can be combined into compound concepts, i.e. concepts that are uniquely defined in terms of elementary concepts., Any union of elementary sets is called a crisp set, and any other sets are referred to as rough (vague, imprecise). With every set X we can associate two crisp sets, called the lower and the upper approximation of X. The lower approximation of Xis the union of all elementary set which are included in X, whereas the upper approximation of X is the union of all elementary set which have non-empty intersection with X. In other words the lower approximation of a set is the set of all elements that surely belongs to X, whereas the upper approximation of X is the set of all elements that possibly belong to X. The difference of the upper and the lower approximation of X is its boundary region. Obviously a set is rough if it has non empty boundary region; otherwise the set is crisp. Elements of the boundary region cannot be classified, employing the available knowledge, either to the set or its complement. Approximations of sets are basic operation in rough set theory. Basics of rough set theory can be found in (Grzymala-Busse, 1988, Grzymala-Busse, 1995, Pawlak, 1991, Pawlak, et al 1995, Slowinski, 1995, Szladow and Ziarko, 1993).