Rough Set Theory with Applications to Data Mining

This paper is an introduction to rough set theory with an emphasis on applications to data mining. First, consistent data are discussed, including blocks of attribute-value pairs, reducts of information tables, indiscernibility relation, decision tables, and global and local coverings. Rule induction algorithms LEM1 and LEM2 are presented. Then the rough set approach to inconsistent data is introduced, with lower and upper approximations and certain and possible rule sets. The last topic is a rough set approach to incomplete data. How to define modified blocks of attribute-value pairs, characteristic sets, and characteristic relation are explained. Additionally, two definitions of definability and three definitions of approximations are presented. Finally, some remarks about applications of the LERS data mining system are included.