Comparisons between Rough Set Based and Computational Applications in Data Mining

Rough set theory is a set theory for the study of information systems which are characterized by insufficient and incomplete information. An information system can be regarded as a set-valued system. Some of its attribute values may be subsets of an attribute domain. One of our objectives of this study is to find rules, relationships and classifications of such a system and to develop applications to data mining. Information systems can be represented in various ways. One approach is to use attribute systems in which each system can be interpreted as an ordered pair (U, R); where U is a non-empty set of all finite objects under consideration and R is an equivalence relation on U. This approach is called the rough set approach. Rough Set theory originated from Pawlak's seminal work (1). It has been conceived as a tool to conceptualize, analyze and classify various types of data. It has been developed as a tool to classify objects which are only roughly described. The available information provides a partial discrimination among them although they are considered as different objects. In other words, objects considered distinct could happen to have the same or similar description, as far as a set of attributes is considered. The theory extends the classical crisp set to a rough (or approximate) set by defining lower and upper approximations for any subset of a non-empty universe. It is based on the concept that every object of the universe is associated with some information (data or knowledge). Objects characterized by the same information are considered indiscernible. Thus an elementary set can be any set of all indiscernible entities, and it forms the basic granule of knowledge (2)-(4). Information granulation is a collection of granules, with a granule being a clump of objects (points) which are drawn toward an object.