Two Interpretations of Rough Sets and Their Application to Preference Modeling

Abstract

We introduce two interpretations of rough sets: rough sets as distinction among positive, negative and boundary regions and rough sets as approximations by means of elementary sets. We show that definitions are different by the interpretations of rough sets under a dominance relation. We apply those two kinds of rough sets to the extraction of if-then rules from a decision table and show the differences between the extracted if-then rules by the interpretations of rough sets.