Rough Sets and Rule Induction by an Approach Based on Coverings in Information Tables
Michinori Nakata, Norio Saito, Hiroshi Sakai and Takeshi Fujiwara
Rough sets, which are a pair of lower and upper approximations, and rules induced from them are described by an approach using coverings in an information table with similarity of values. Lots of possible coverings on a set of attributes are derived in an information table with incomplete information, whereas only one covering is derived in an information table with complete information. New difficulty due to computational complexity is not caused in any information table with incomplete information because of the lattice structure that the family of possible coverings has. Twofold rough sets are derived, which consist of certain rough sets and possible rough sets, using only the minimum and maximum possible coverings. These two possible coverings are obtained from the minimum and the maximum possible indiscernibility relations which are equal to the intersection and the union of indiscernibility relations derived from possible tables. Four kinds of rules with accuracy and support are induced from the twofold rough sets. The computational complexity for the number of objects in incomplete information tables is the same as in complete information tables.
Keywords: Twofold rough sets, Rule induction, Incomplete information, Coverings, Indiscernibility relations