AbstractsMathematics

Rough set theory offers a mathematical approach to data analysis and data mining. It can be used to learn classification rules that define classes of a classi- fication based on some well defined concepts. The fundamental task of rough set data analysis is to precisely construct and interpret concepts. When applying rough set theory to rule learning, the main tasks involve removing redundant attributes, redundant attribute-value pairs, and redundant rules in order to obtain a minimal set of simple and general rules. Following Pawlak, we can arrange these tasks into a three-step sequential process, called Pawlak three-step approach, based on a central notion of reducts. One problem is that reducts used in the three steps are de fined and formulated differently. Such an inconsistency in formulation may unnecessarily affects the elegancy of the approach. By adopting the classical view of concepts that interprets a concept by a pair of intension and extension, in this thesis we introduce a generic definition of reducts of a set. We define various reducts used in rough set analysis in a uni ed way. We study several mathematically equivalent, but differently formulated, definitions of reducts. Each definition captures a different aspect of a reduct and their integration provides new insights. The Pawlak three-step approach is reformulated uniformly as a search for different reducts.