Rule induction based on rough sets from information tables containing possibilistic information

How rules are induced on the basis of rough sets has been examined in possibilistic information systems where attribute values are expressed by normal possibility distributions. We cannot obtain the unique membership degree of an object for rough approximations in the possibilistic information systems. Instead, we can derive certain and possible membership degrees to which an object certainly and possibly belongs to rough approximations. The certain and possible membership degrees are lower and upper bounds of the actual membership degree. Using the certain and possible membership degrees, we express rough approximations in possibilistic information systems. The rough approximations consist of objects with membership degrees described by not a single, but an interval value. This leads to that lower and upper approximations are linked with each other. Next, we show that it is not sufficient to use the rough approximations in order to obtain objects certainly supporting a rule. To solve the difficulty, we formulate rough approximations under considering characteristic values of equivalence classes. Furthermore, we introduce a criterion for valuable rules. Our approach is free from the restriction that possibilistic information appears in some specified attributes. Therefore, we can induce valuable rules that hold between arbitrary set of attributes in possibilistic information systems.